This work presents numerical methods of calculation of earthquake resistance of shells of revolution based on the application of the theory of random processes combined with the FEM. Probabilistic character of seismic effect is determined by using artificial accelerograms based on stochastic process. To illustrate the above methods of probabilistic analysis of seismic stability of structures, two real objects and one projected one are considered. Displacements, stresses, forces and moments resulting from the action of seismic load have been determined. Comparison of the results of calculation with those achieved using calculation of prescribed real accelerograms and building design codes have been made. Comparative analysis of the calculation results brings us to the conclusion that the difference between the results obtained using different methods can be quite significant. It means that when designing structures of the types of shells of revolution under consideration it is necessary to do calculations using all methods recommended by design codes as well as probabilistic methods.