The three-dimensional (3D) finite element model of shape memory alloy (SMA) joint system under a clamped-clamped support was established. Using the coupled thermal-mechanical transient state analysis, stress distributions of models under the different loads (internal pressure, temperature) were investigated. And the temperature field, thermal strain field, stress and creep of the joint system were obtained. The results show, 1) for the non-coat SMA joint system, the interface in middle region of the joint’s internal wall is the dangerous region. In this region, the joint’s adhesion failures easily occur and the crack easily initiate. The joint’s coat can improve the fatigue life of joint system. 2) There are higher levels of radial temperature gradient, temperature strain and temperature stress between the internal and external walls of the joint. The creep strain in the internal-external walls of the joint is the main reason for adhesion failure in middle interfaces between the joint and the pipe.