Non-linear behavior of soils during a seismic event has a predominant role in current site response analysis. Soil response analysis consistently indicates that the stress–strain relationship of soils is non-linear and shows hysteresis. When focusing on forced response simulations, time integrations based on modal analysis are widely considered; however, parametric analysis, non-linear behavior and complex damping functions make difficult the online use of standard discretization strategies, e.g., those based on the use of finite element. In this paper, we propose a new harmonic analysis formulation, able to address forced response simulation of soils exhibiting their characteristic non-linear behavior. The solution can be evaluated in real-time from the offline construction of a parametric solution to the associated linearized problem within the Proper Generalized Decomposition framework.