The variant of semianalytical method of finite elements for computation of cylindrical shells subject to dynamic influence is developed, at the axisymmetric stress-strain state In the plan of construction the functions sought after are approximated by linear polynomials, and on a thickness are searched on the basis of decision of the proper system of differential equalizations. With the use of the developed method the analysis of the stress-strain state of cylindrical shells under act of the local dynamic loading is conducted. The necessity of consideration of three-dimensional character of deformation at the decision of a similar class of tasks is shown.