This paper presents a method capable of evaluating the seismic stability of a cut slope formed by strain-softening soil; to date, no method appears to be available for this purpose. The method consists of the following steps : (1) the horizontal vibration of a sliding mass subjected to an earthquake loading is converted into an equivalent single-degree-of-freedom (SDF) system with a smooth hysteretic restoring force; (2) a failure criterion and a damage index for the converted SDF system is established; and (3) the safety based on the response statistics obtained through random vibration analysis is evaluated. Reliability against sliding failure is assessed for specified intensity and duration of a seismic loading using results from a nonlinear-hysteretic random vibration analysis.