<p>This paper provides analytical solutions for a power cable joint’s steady and dynamic thermal stress problems. This study offers an innovative refinement of current approaches for calculating the change of interface pressure in power cable joints due to thermal cycling. This approach incorporates elastic modulus and thermal expansion of the insulating materials as functions of temperature. Cable joints are examined in both air and soil environments, with configurations both including and excluding a sheath. The radial stresses are calculated for three interfaces: cross-linked polyethylene- Ethylene Propylene Rubber XLPE-EPR, XLPE-XLPE, and EPR-EPR. The final results suggest that a softer material, characterized by a lower elastic modulus, exhibits more stable behavior with minimal variations in initial pressure, especially when the elastic modulus remains consistent and thermal expansion is low. Results reveal the significant effect of the temperature-dependency of the material properties on the change of interface pressure. The same problem is analyzed in the dynamic state by incorporating thermal capacities, with the change of interface pressure examined under the assumption that both the elastic modulus and thermal expansion are temperature-dependent. The heat equation is solved twice, followed by the solution of the equation for a deformable body using the finite difference method (FDM). The model was subsequently compared with a finite element model. The required computational time and allocated computer memory are much reduced when using FEM. This dynamic model effectively fulfills the requirement for dynamically approximating the change of interface pressure during thermal cycling.</p>