This study evaluates adhesively bonded pipes with curved-surface lap joints subjected to internal pressure. To test the effects of curvilinear radii on the strength of the adhesive bond, steel pipes (St 37) with curved surfaces of the same lap length and different radii were bonded with the adhesive DP 810. Internal pressure was applied until failure and the mechanical behavior of the bonds was examined experimentally and numerically. Numerical analyses used Cohesive Zone Materials Models (bilinear, exponential, and mixed mode) to estimate the strength of the adhesive bonding. The parameters required for material models were determined experimentally and then experiments were run to verify the models with the finite elements. The results show that the curvature radius has considerable influence on failure pressure.