This thesis covers the numerical analysis of the supporting structure of a furnace in a steam boiler operating on solid fuels. The numerical analysis is performed utilizing two computational packages employing the Finite Element Method (FEM) for structural analysis: CATIA and Abaqus. A brief overview of thermal power plants is given, outlining the major differences in design and construction of such plants. A more detailed description of a combustion system featuring a grate firing design used for solid fuels is presented. Two simplified models were used for the purpose of verifying numerical simulation and finite elements used in the analysis. The verification process was performed by comparing the results of the analytical analysis of the two verification models with the appropriate results of the analyses performed in the aforementioned computational packages and displaying the convergence of finite elements for each model. Furthermore, a 3D representation of the boiler was modeled based on the given industrial documentation and a simplified 3D model was created retaining only the necessary design features affecting the the stability of the structure and the structural analysis in general. One half of the simplified model was used for numerical simulations in both computational programs (CATIA and Abaqus). A mesh sensitivity study was performed using four models with varying mesh density near the regions of increased concentration of stresses. The final results of the numerical analyses are presented and verified against the currently valid norms.