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Analytical formulas for calculating the maximum velocity of penetration of doublelayer cermet and ceramic/organic-plastic targets are obtained taking into account the structural characteristics of the target and the physical and mechanical properties of the projectile and target materials. Using these formulas, the ballistic resistance of targets was studied and the possibility of optimizing their structure was shown. The results agree qualitatively with available experimental data. The optimal relative thickness of the ceramic layer which provides maximum penetration velocity was determined at areal densities of the target of 30-50 kg/m for different substrate materials. It is found that these velocity values depend weakly on the areal density of the target and are mainly determined by the properties of the substrate material. [ABSTRACT FROM AUTHOR]