This paper proposes a new deterministic envelope function to define non-stationary stochastic processes modeling seismic ground motion accelerations. The proposed envelope function modulates the amplitude of the time history of a stationary filtered white noise to properly represent the amplitude variations in the time histories of the ground motion accelerations. This function depends on two basic seismological indices: the Peak Ground Acceleration (PGA) and the kind of soil. These indices are widely used in earthquake engineering. Firstly, the envelope function is defined analytically from the Saragoni Hart’s function. Then its parameters are identified for a set of selected real records of earthquake collected in PEER Next Generation Attenuation database. Finally, functions of the parameters depending on the Peak Ground Acceleration and the kind of soil are defined from these identified values of the parameters of the envelope function through a regression analysis.