Large scale dynamic finite element analysis of complex nonlinear mechanical or structural systems can be very expensive. To significantly reduce the computational cost various techniques have been developed and presented in the literature. The reduction method based on symmetry group or the so-called group theoretic approach (GTA) of Healey and associates for bifurcation analysis and free vibration analysis of geometrically nonlinear systems with symmetries has been extended by the authors to deal with transient geometrically nonlinear response of structures discretized by the finite element method (FEM). Computed results for two discretized space trusses were obtained with the GTA, and presented by the authors in a previous paper. Application is further made of the GTA for the computation of geometrically nonlinear response of beam and membrane structures during the second phase of the investigation reported here. The obtained numerical results indicate that the GTA can be applied to relatively more complicated structural systems that include symmetry of nodal rotations. It was observed that the results obtained by the GTA are very accurate and the GTA is very efficient compared with technique for the full space problems.