The system of nonlinear equations modeling the process of nonstationary stimulated Raman scattering (SRS) in noncentrosymmetric crystals for the waves on laser, Stokes, polariton, and phonon frequencies is investigated by using the numerical methods. The general case for amplitudes of waves that resulted in doubling of the number of equations is considered. It is shown that the application of the methods of finite differences to the computer simulation of transition regimes is completely consistent with the analytical results found for the asymptotical solutions in form of solitons. The obtained results also indicate that the laser pulses of Gaussian shape appearing at the boundary of nonlinear medium tend to become solitons of Lorentzian shape. It was also found that the formation of solitons occurs when the vibrations of optical phonons and that of electromagnetic wave were either in or out of phase. It is shown that all electromagnetic waves entering the medium with different speeds become solitons having the same speed. In the second part of the paper we considered the computer simulation of soliton stability with respect to small (weak) perturbations of all interacting waves. In the present paper we considered the case of evolution of those disturbances in the vicinity of peaks of solitons. The numerical analysis showed that in wide range of parameters the solitons were stable.