Prismatic shells find wide application in mechanical, civil and aeronautical engineering. The object of this paper is to propose a method of analysing such shells having different internal ribbing for their torsional vibrations. The governing equations of motion are derived by using a finite difference method and solved by the simultaneous iteration technique. The accuracy of the method is ascertained by comparing the results for some wellknown boundary conditions with the results obtained by classical methods. Shells of square cross-section and rectangular shells of variable and constant cross-section have been analysed. The effects of introduction of diaphragms on the eignefrequencies have been analysed. The effects of variations in shell thickness and length on the dynamic behaviour also have been studied. © 1975 Academic Press Inc. (London) Limited.