Bifurcation buckling will occur under internal pressure in the top end closure of cylindrical oil storage tanks with fixed roofs. In the design of the tanks, the shell-to-roof joint is considered frangible and is expected to fail before failure occurs in the shell-to-bottom joint. This paper describes the buckling analysis of the top end closure of the tank. The influence of both the tank diameter and the slope angle of the roof on the buckling internal pressure is investigated by the axisymmetric finite-element method. Large-deflection elastic analysis in the prebuckling state is performed. The values of the buckling pressure obtained by FEM are compared with those calculated by a formula of API standard 650, which is a design code for the oil storage tanks. Results show that the API formula gives smaller buckling internal pressure than FEM in the range of the small tank diameter, and seems to underestimate the pressure from the viewpoint of the frangible joint.