It is well known that the non-stationary nature of earthquake motion is intensely controlled by the phase spectrum. However, it has not yet been verified how the stochastic characteristics of phase spectrum of such motion affects the response of structures. We therefore modeled the stochastic characteristics of the phase spectrum, and derived a theoretical solution for mean and R.M.S. response time histories for an SDOF system excited by a non-stationary input ground motion controlled by these stochastic phase characteristics. We also derived a methodology to estimate the peak response value using the concept of a complex envelope function.