Initial conditions on the computation of response spectra are unknown in the case of analog earthquake records that have lost the initial portion of motion and assumed to be zero for calculation purposes. This assumption, rigorously speaking, is only valid for high-frequency systems, such as rigid structures. Both rigid and flexible structures are sensitive to the initial conditions of the motion. The spectral values for long period, elastic or inelastic systems tend to be particularly sensitive to the initial conditions of motion. Unconservative designs of long period structures may result if the initial condition effects are not properly accounted for. In this paper two approximate methods are developed to approximate the true “non-resting” response spectra from the conventional ones and a given set of initial conditions. As expected, these conditions clearly control the free vibration part of the response of long-period systems, as opposed to short-period systems which are governed by the transient phase of the response.