A dynamic behavior of solid propellant motor composite casing under the action of an internal impact pressure is treated. This pressure describes the engine operation. The thin-walled casing consists of the cylindrical shell and two bottoms. These bottoms are truncated hemisphere. The casing is clamped along two edges of the bottoms. A shear, a rotary inertia and stress–strain relations for an orthotropic material are accounted. Semi analytical method is suggested to analyze the structure stress–strain state. The thin-walled casing dynamic is described by large dimension system of the ordinary differential equations.