The monograph is based on the results of the authors obtained during the last decade and only partially published in scientific periodicals. Part I presents some common methods of engineering penetration modeling. Particular attention is given to two closely related approaches: the localized interaction and cavity expansion approximations that are widely used in the monograph. In this part for the first time appears a comprehensive description of the localized interaction approach and the tools for its application to penetration mechanics. Part II is devoted, mainly, to shape optimization of impactors applied to different media (metal, concrete, FRP laminate) and using different impactor-shield interaction models. Part III deals with analysis and optimization of multi-layered shields against ballistic impact. In this part of the monograph the influence of the order of the plates in the shield and of the spacing between the plates on the ballistic parameters are studied. This part includes the analysis of the optimum structure of metal/ceramic shields. Although the emphasis in the book is on the analytical methods, rigorous mathematical proofs and numerical simulations complement each other in the book, and the results are presented in an illustrative manner. The monograph is self-contained and assumes only basic knowledge of solid mechanics and mathematics. The brief exposition of the necessary additional information is presented in the book.