To consider fatigue and design problems, the authors apply statistical and optimization methods. The book consists of four chapters and seven appendices. In chapter 1, “Data reduction”, several probability distributions are defined, e.g. Gaussian and Weibull distributions together with the concepts of confidence intervals and goodness of fit testing. Chapter 2, “Application of probability to mechanical design”, presents and discusses several formulae of probability calculations. Fatigue behavior and fatigue properties of materials are considered by means of statistical methods, and applications of Monte Carlo method to fatigue calculations are illustrated. Examples of optimal design are given in chapter 3, “Optimum design”. The novice level ideas of linear and nonlinear optimization methods are introduced and several examples of geometric programming are presented. Finally, chapter 4, “Reliability”, briefly reviews the history of increasing reliability of technical systems. Reliability and mean time to failure are calculated for several technical systems. Appendices contain data of the problems described in the main text, and references to software packages. The book is intended for the use by practicing engineers in industry, and is prepared as a textbook including many exercises and problems.