The seismic design of structures has been evolving and taking new ways; as a consequence, new tendencies are aiming at controlling the deformation that structures experience when they undergo seismic loads, since it is with deformations where structural and non-structural damage can be determined. Control of deformations has been studied and presented in what is known today as Performance-Based Seismic Design, which has caused a change in the traditional design philosophy that is forced-based, and in turn, it has demanded changes in the seismic loads represented in the response spectra of any nature. This work focuses on obtaining elastic displacements response spectra that can be used in the displacement-based seismic design proposed for Kowalsky and Priestley (2000), where the displacement is the input parameter for the application of this methodology. For this purpose, a methodology consisting of two parts was used: a) seismological; represented in the adjustment of the free parameters that control the form of the Fourier amplitude spectra (FAS) to be used in the simulation of strong motion using stochastic methods and b) the obtaining of response spectra for soil deposits of Armenia city. As a consequence, 24 synthetic signals were obtained for the M-d couple, consistent with the regional seismic hazard, using Boore's (2000) software for stochastic simulation SMSIM. This software is based on the seismological model of the radiated spectrum for the simulation of ground strong motion. Since the generated signals using this methodology do not take into account site effects; namely, the amplification of the seismic waves in specific soil deposits, it was necessary to filter these synthetic signals through the soil deposits in city of Armenia (Ingeominas, 1999). Consequently, it was possible to generate signals that allowed obtaining displacement response spectra consistent with the seismic code that regulates the seismic design in Armenia (Decree 079, 1999). Both displacement response spectra and displacement design spectra for three zones were generated (zones A, B and C); all of them were defined for six levels of damping, appropriate to be used for displacement-based seismic design in Armenia.