There are two types of books that you need for the Machine Design & Materials PE exam. You need study material and references. Study materials include practice exams and study guides that will help to teach you the material necessary to pass the PE exam. References are books that contain equations, tables and large amounts of data in all sorts of topics related to Machine Design & Materials. I will go through the books that you need in both study material and references that are either free or cheap.

You should spend only around $260 to $300 TOTAL on study material and references. I don’t think that you should spend $1,000s on material that you will only use once in your life.

NCEES Machine Design & Materials Sample Exam ($53)

The sample exam provided by NCEES is the best way to figure out the type of problems that will be on the exam. You can also get a sense for the level of difficulty. The cost of this book is $40 and you get 80 problems. But this cost does not include shipping. The total cost with shipping to most places in the US is around $53. If you buy this book on Amazon with shipping, then the cost is roughly $70. You can check EBay for this book, but at the time of this post I was unable to find this book on EBay.
Link: https://account.ncees.org/exam-prep/339

NCEES Machine Design Materials Outline (Free)

The outline should be used to help guide your studying of the following materials and references. As you go through the material, you should only focus on the topics that are within this outline. This will help to save time. For example, you do not need to know complex math topics, fluids, ethics, etc.
Link: https://ncees.org/wp-content/uploads/PE-Mech_Machine-Apr-2017.pdf

Engineering Pro Guides Technical Study Guide ($40)

This technical study guide takes you through the key concepts and skills necessary to pass the PE exam and also has some problems. The guide follows the previously mentioned outline and is very comprehensive. You will have to find a way to print it out, because it is only PDF, but it is also very cheap at only $40 for around 400+ of specific content for the PE exam. It gives you all the important equations, formulas and terms. It also has a lot of figures to help explain all the concepts and skills that you need to pass the exam.
Link: https://engproguides.com/pe-mechanical-machine-design-and-materials-practice-exam-guide.html

Engineering Pro Guides Full Exam ($40)

You will need more problems besides the NCEES sample exam to practice and to hone your skills. Engineering Pro Guides has the cheapest exams. It is $40 and has decent reviews and you are also able to ask questions from the author. Other exams cost around $59 to $100. The Engineering Pro Guides are closer in difficulty to the NCEES sample PE exam. The other exams are more difficult. You can also search for free exams online that do not come with solutions. Other ways to get more problems are to do the problems within the references below. Make sure to focus on the topics in the NCEES outline when you do those problems too.
Link: https://www.engproguides.com/pe-mechanical-machine-design-and-materials-practice-exam.html

Machinery’s Handbook from EBay ($65)

The Machinery’s Handbook is one of the best references to be used on the PE exam. It contains many material properties for the common materials. It contains a lot of formulas and equations for the various types of mechanical components. On Amazon, this book is around $100, but you can get older versions for much cheaper like this one below from EBay. You may think that you need the newest and latest version to pass the exam, but in my opinion you don’t. Just think about all the other people that passed the exam previously with older versions of this book. Engineering and science is not going to change drastically, all the formulas, equations and material properties are still the same.

Please make sure that you do not buy the pocket version or toolbox version because the print is too small. Also do not buy the guide, make sure you are buying the full print, large text version.
Link: https://www.ebay.com/bhp/machinery-s-handbook

Shigley’s Mechanical Engineering Design from Amazon Used ($105)

Shigley’s Mechanical Engineering Design contains the other half of the information required to pass the PE exam. The Machinery’s Handbook contains the first half. This book covers bearings, gears, springs, belts, pulleys, power screws, shafts, keys, welding, fastener groups, bolts, screws and rivets. I have this book because I had a college course on this topic. This book covers many of the topics from the NCEES outline.
Link: https://www.ebay.com/sch/i.html?_from=R40&_trksid=p2053587.m570.l2632.R2.TR10.TRC1.A0.H0.Xshigley.TRS0&_nkw=shigley%27s+mechanical+engineering+design&_sacat=2228

Websites (free)

The last set of references include the websites that apply to the NCEES outline topics that are not covered in Shigley’s or Machinery’s Handbook.

Interpretation of Technical Drawings

This topic requires you to be able to read machine design drawings. You should have this welding symbol chart to help you with a drawing that has welding. You should also be familiar with geometric dimensioning and tolerances, also minimum material condition.
Link: https://app.aws.org/mwf/attachments/64/225364/AWSWeldSymbolchart.pdf
Link: https://app.aws.org/itrends/2009/07/it200907/it0709-14.pdf
Link: https://www.gdandtbasics.com/gdt-symbols-chart/

Quality Assurance & Quality Control

There may be a couple of questions that require you to use control charts, so you should have a copy in your references.
Link: https://www.stat.auckland.ac.nz/~wild/ChanceEnc/Ch13.pdf
Link: https://web.mit.edu/2.810/www/files/readings/ControlChartConstantsAndFormulae.pdf

Project Management

There may be a question on Project Management on the exam.
Link: https://www.math.upatras.gr/~tsantas/DownLoadFiles/hil61217_ch22.pdf

Beam Formulas

This is a helpful cheat sheet of the common beam arrangements and the corresponding equations.
Link: https://www.awc.org/pdf/codes-standards/publications/design-aids/AWC-DA6-BeamFormulas-0710.pdf

Economics

There might be one question that requires you to use the economics factor tables.
Link: https://global.oup.com/us/companion.websites/9780199778126/pdf/Appendix_C_CITables.pdf
Link: https://www.webpages.uidaho.edu/~mlowry/Teaching/...

Vibration

These vibration isolator manufacturers provide step by step instructions on how to size and select isolators.
Link: https://www.novibes.com/images/2017%20Catalog.pdf
Link: https://www.cooperindustries.com/content/dam/public/bline/Resources/Library/catalogs/pipe_hangers/pipe_hangers_and_supports/VibraTrol.pdf

Hydraulic Components

There might be one question that requires you to use the economics factor tables.
Link: https://global.oup.com/us/companion.websites/9780199778126/pdf/Appendix_C_CITables.pdf
Link: https://www.webpages.uidaho.edu/~mlowry/Teaching/...

Pneumatic Components

Atlas Copco is a leading manufacturer in compressed air. They provide a very detailed PDF on compressed air.
Link: https://www.atlascopco.com/content/dam/atlas-copco/local-countries/egypt/documents/Compressed_Air_Manual_tcm44-1249312.pdf

Shear Flow

These websites provide more information on how to calculate shear flow for fasteners and adhesives.
Link: https://abe-research.illinois.edu/faculty/dickc/Engineering/shearflowa.htm
Link: https://www.assakkaf.com/Courses/ENES220/Lectures/Lecture14.pdf
Link: https://www.engr.psu.edu/lcvideos/emech210/beam_shear_stress/...

Testing and Instrumentation

You should have an idea of the equipment and testing process for the various material properties like hardness and ultimate tensile stress. The best place for this information is to go straight to the testing equipment manufacturers’ websites.
Link: https://www.ametektest.com/products
Link: https://www.nde-ed.org/GeneralResources/MethodSummary/MethodSummary.htm
Link: https://www.ametektest.com/learningzone/testtypes