This paper develops a probabilistic methodology for the seismic reliability analysis of structures with random properties. The earthquake loading is assumed to be described in terms of response spectra. The proposed methodology takes advantage of the response spectra and thus does not require explicit dynamic analysis of the actual structure. Uncertainties in the structural properties (e.g. member cross-sections, modulus of elasticity, member strengths, mass and damping) as well as in the seismic load (due to uncertainty associated with the earthquake load specification) are considered. The structural reliability is estimated by determining the failure probability or the reliability index associated with a performance function that defines safe and unsafe domains. The structural failure is estimated using a performance function that evaluates whether the maximum displacement has been exceeded. Numerical illustrations of reliability analysis of elastic and elastic-plastic single-story frame structures are presented first. The extension of the proposed method to elastic multi-degree-of-freedom uncertain structures is also studied and a solved example is provided.