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Some problems of multipurpose analysis and optimization of deformed structures and thin-walled structural elements are studied in this paper under some constraints including incomplete data. The first problem is the multipurpose optimization of layered plate made from given set of materials in context of optimization of ballistic limit velocity. Incomplete data concerning the thickness of layers of optimized multilayered shield structure are taken into account. The Pareto-approach and numerical evolutionary method (genetic algorithm) are used for solving of the considered multipurpose problem. The second problem studied in the paper is the shape optimization problem for rigid punch moving on the surface of elastic half-space, which is solved analytically in multipurpose formulation taking into account friction of contacted surfaces, wear of materials and arising pressure distributions. The relative movement is considered in frame of quasi-static formulation. Formulated optimization problem is studied analytically using the developed decomposition approach and exact solutions are obtained for the punch which has a rectangular contact region and moves translationally with a constant velocity.