Wave-propagation equations of nonreciprocal cylindrical helix phase shifters are conventionally solved using mathematical functions, for which extensive tables are not easily available. The finite-element method (FEM) appears to be a comparatively easier means of solving these problems. The paper describes the application of the finite-element method to a very complex problem: a gyromagnetic medium with periodically varying spatial boundary conditions. The results of finite-element analysis of a normal, an inverted and a ferrite-embedded helix ferrite phase shifter in circular cylindrical geometry are presented. The relative effectiveness of these three phase shifters is studied to show that the differential phase shift is large in the case of the normal helix compared with the inverted helix.