This thesis covers the master diploma work conducted at Hohai University, Nanjing, People's Republic of China. An overflow spillway section fitted for the Longtan Dam was designed and the loads acting on it was identified after an iterative flood routing calculation. The section was then evaluated, both theoretically and numerically using FEM with a linear-elastic isotropic constitutive model, with regards to the stability against compressive and tensile failure. Also, a numerical analysis of the seepage through and around the structure was conducted. The results show that, for a given design of the section, the structure can handle the compressive stresses that arises. However, the numerical analysis indicates a possible tensile failure at the dam heel, which is inconsistent with the theoretical stability analysis. The seepage analysis show that the maximum seepage occurs at the dam heel, the dam toe, and at grout curtains beneath the structure. A simple convergence analysis was done which showed stress singularities at the dam heel and dam toe. These were discussed and connected to the St Venant's principle, and these singularities shows the risk of blindly trusting numerical results.