Shape memory alloys are used in medical domain and engineering fields’ especially in aeronautic industries, robatics, civil and loom engineering due to their distinguished features than ordinary metals. The lack of knowledge caused by the inability of their fatigue life prediction extremely shows off due to the pace of technological developement and vast technological use of these alloys. In recent decades, many researchers concentrate on study of their behavior. Recently, investigation of their fatigue and the effective parameters on this phenomenon has become a popular research topic. Accordingly, fatigue of CuAlBe alloy and the influence of parameters like stress and loading frequency on its fatigue life are studied in this thesis. Study of the loading frequency effect is one of the main aims of the present thesis, since temperature variations affect their behavior saliently and the frequency leads to significant changes in such a sample temperature. Furthermore, a few authors can observe and investigate the direct effect of this parameter. According to distinct behavior of the studied alloy than of NiTi, usual phase diagram is modified to predict phase transformation. One of the weaknesses in scientific field of studying these alloys’ cyclic behavior is the absence of a capable constitutive model to predict their behavior, thus, most results are experimentally achieved. In this regard, the only existant and used constitutive model is formed on the base of experimental observations and not in a continuum framework. This model has predicted fatigue life with use of a parameter called stabilized dissipated energy. In the present work, a fully-coupled thermomechanical model which is presented in a continuum framework is employed to predict the wire sample behavior and results of this model are compared with experimental one to verify the model. After verification of the numerical results, a cycle-dependent phase diagram is presented and used to formulate cycle-dependent parameters in this diagram as well as stabilized dissipated energy. Finally, a relation for fatigue life prediction of specimen is generated with the stabilized dissipated energy’s formula. In this relation, the effect of stress and loading frequency is clearly observed on fatigue life. Since tension-compression test is one of the most usual and simplest possible types of experiments, the experimental results are developed by applying tensile loading on the specimen. Key Words Shape memory alloys, Fatigue life prediction, Stabilized dissipated energy, Loading frequency, Cycle-dependent phase diagram, Uniaxial tension-compression loading.