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 is applied in the investigation reported here to the computations of responses of geometrically nonlinear systems under intensive transient excitations. A digital computer program written in Fortran language has also been developed for the work. Two space trusses discretized by the finite element method are chosen to illustrate the use of the GTA for cases undergoing large deflections. In the response computations for both the full space and reduced space or subspace problems the central difference method is employed. Numerical results are obtained. Comparisons of results for full space problems to subspace problems are made. It is concluded that the GTA is mathematically very elegant and rigorous. Computationally, the solution is exact and it is very efficient for geometrically nonlinear systems undergoing large deformation. The GTA is currently being developed for the response analysis of geometrically nonlinear systems with partial symmetries.