The stress evolution occurring in UMo/Al dispersion fuel is important since it affects the fuel performance during irradiation. In this study, a new analytical model was developed to predict the local stresses in UMo/Al dispersion fuel. In the model, a hypothetical unit sphere composed of a UMo fuel particle, interaction layer (IL), and Al matrix was considered, and the governing equations for the stress-strain relationship, strain-displacement, and mechanical equilibrium were established using a spherical coordinate system. The mathematical derivations were obtained for local stresses in the radial and circumferential direction using a thick-walled sphere model. This analytical model employed the stress distribution as the boundary condition, which is calculated using a finite element model with homogenized fuel meat. The developed model’s solution scheme was verified against Abaqus solutions obtained for two irradiated plates with heterogeneous meat. The model calculated consistent results for interfacial stresses in the IL and Al matrix, indicating that the newly developed model was reliable when simultaneously calculating fission gas pressurization on the UMo/IL/Al composite, and the use of the stress distribution in the homogenized fuel meat as the boundary condition for the analytical model was acceptable.