A numerical analysis of complex axisymmetric structures subjected to arbitrary loading is presented. The analysis is carried out with the aid of a semianalytical finite element method within the framework of a linear model of orthotropic material with allowance for four types of elements. The numerical integration of the equations of motion is performed using alternatively two algorithms. The direct integration method and the mode superposition method. The validity of the analysis is illustrated by a number of numerical examples calculated by the computer program DYNAX-L written in FORTRAN-IV.