In the present work, an elasto-plastic model is proposed for the numerical analysis of dynamic nonlinear behavior of composite thick shells with reinforcements in spirals subjected to impulsive loading. Wilkins algorithm was taken to analysis physical and geometrical non-linearity of stress-strain state of elasto-plastic thick composite shells. This study is carried out on two types of cylindrical composite shells in different reinforcement winding angles and different magnitudes of impulse loads. By a calculation code in finite difference, first the influence of physical non linearity on the stress-strain state of cylindrical monolayer shell was established and then the relationship between residual strains and the winding angle of the symmetric reinforcements was investigated. Finally, the influence of the winding angle of the orthogonal reinforcements on the residual strains of a bilayer composite shell was analyzed numerically.