Axisymmetric finite element model of packer rubber cylinder was established by using the hyperelastic material Mooney Rivlin in ANSYS, the distribution rules of stress and deformation along rubber cylinder’s length under different temperature load were analyzed. The results show that temperature has certain effects on stress distribution of packer rubber cylinder, at room temperature (25 ℃), the upper rubber cylinder has uniform stress distribution along its length, the stress of intermediate rubber cylinder is less at both ends and bigger in the middle. The maximum stress is in the outside surface of lower rubber cylinder bottom and the minimum stress is in the inner surface, the stress values are 19.693 MPa and 3.984 MPa separately. With the increase of temperature, the stress distribution in intermediate rubber cylinder tends to be uniform, and the stress at outside surface of lower rubber cylinder bottom is increased and reaches 19.712 MPa at 100 ℃. The deformation of rubber cylinder along its length is nonlinear, the upper rubber cylinder has smaller deformation and the deformation is increased along rubber cylinder’s length, the intermediate rubber cylinder has maximum deformation, the deformation value is 9.17 mm. The temperature has smaller effect of on the lower rubber cylinder, the deformation is smaller and the change is relatively stable.