The overwhelming majority of studies in microelectronics and fiber-optics are experimental. Not too many apply numerical, mainly finite-element, methods to analyze microelectronic and fiberoptic structures. There is a very small number of papers using analytical modeling. At the same time application of powerful and well-developed analytical methods of Engineering Mechanics often enables one to obtain valuable prior information of the mechanical behavior of materials and structures, interpret empirical data, and to extrapolate the accumulated experience on new designs [1,2]. As a rule, application of analytical modeling results in better understanding of the behavior and performance of a material or structure, and in substantial savings of time and expense. This review, based primarily on the author's research, addresses several basic and practically important problems related to the mechanical behavior of materials and-rational structural design of microelectronic and fiber-optic systems and lending themselves to sufficiently simple analytical solutions.