We simulate numerically behavior of an explosive solid fuel fastened to a two-layer shell during high-speed impact. The layers made from orthotropic organo-plastics. We study how the orientation of elastic and strength properties of the materials affects stress-strain state of a solid fuel during an impact of a steel isotropic sticker against a booster engine. We consider both normal and oblique impacts. The investigation was performed in the framework a phenomenological model of solid mechanics. We employ a variant of finite element method to analyze three-dimensional problems. It is shown that shock waves may attenuate in structural elements made from anisotropic materials and we have an opportunity to control this attenuation varying orientation of properties of materials with respect to the solid fuel and the direction of a load applied.