In LD end-pumped solid-state laser, the crystal rod is held and cooled by the metal heat sink. The force applied to the side surface of the crystal is non-axisymmetric. Under such circumstances, three kinds of thermal contact conductance (TCC) models are established, including not using thermal interface material, using thermal interface material with its thickness equal to the average thickness of the gaps and using thermal interface material with its thickness much greater than the thickness of the gaps. Regarding to the first two models, the influences of the assembly force and the equivalent root-mean-square (RMS) roughness on thermal contact conductance are discussed based on the Truncated-Gaussian model and the plastic-deformation model. The contact heat dissipation model of the crystal rod and the heat sink is established. For the Gaussian heat consumption, the spatial distributions of temperature inside the crystal with and without thermal interface material are obtained by the finite element method. The results show that without thermal interface material, the thermal contact conductance between the crystal rod and the heat sink changes significantly in the circumferential direction, which reaches a maximum on the bottom of the heat sink groove and a minimum on the contact area of the heat sink couple. With the assembly force increasing and the equivalent root-mean-square roughness decreasing, the thermal contact conductance gets larger and more nonuniform, and the temperature of the whole crystal rod reduces. When the indium foil is used as thermal interface material, the thermal contact conductance gets larger and more uniform, the temperature of the whole crystal rod reduces as well and its distribution is axisymmetric.