Intelligent and adaptive material systems and structures have become very important in engineering applications. The basic characteristic of these systems is the ability to adapt to the environmental conditions. One of the new class of materials with promising applications in structural and mechanical systems are Shape Memory Alloys (SMA). The mechanical behavior of shape memory alloys in particular shows a strong dependence on temperature. This property provides opportunities for the utilization of SMAs in actuators or energy dissipation devices. However, the behavior of systems containing shape memory components under random excitation has not yet been addressed in the literature. Such study is important to verify the feasibility of using SMAs in structural systems. In this work a non-deterministic study of the dynamic behavior of a single degree-of-freedom (SDOF) mechanical system, having a Nitinol spring as a restoring force element is presented. The SMA spring is characterized using a one-dimensional phenomenological constitutive model based on the classical Devonshire theory. Response statistics for zero mean random vibration of the SDOF under a wide range of temperature is obtained. Furthermore, nonzero mean analysis of these systems is carried out.