The paper is devoted to stochastic foundation impedance modeling for buildings submitted to vibrations.The hidden-variables method used in seismic engineering is revisited, due to a larger frequency range used in vibration prediction. Indeed,in this new context, instability of the solution and non-physicalnature of mass and stiffness random matrices have been observed. The hidden variable method has been therefore implemented by enforcing explicitly the stability of the solution and the positiveness of mass and stiffness matrices.The effects of numerical parameters used throughout the process are shown and the improved hidden-variables method has been used for predicting the level of vibrations inside a building induced by railway sources. We present here steps of stabilization process, and then discuss on an example of application.