The analytical evaluation and finite element methods are used to analyze the critical stability of the shallow spherical roof of oil storage tank with an axial symmetrical corrosion region. At first, the nonlinear finite element method is adopted to calculate the global critical load of the storage tank roof, and the local corrosion region is equivalent to a circular corrosion pit with uniform depth. The results show that the tank wall and inner pressure of the stored oil have slight effects on the stability of the roof. To build the formula of local critical load of the tank roof, the circular corrosion pit is separated from the whole roof and treated as a shallow spherical shell which is elastically supported on the rest part of the roof. The equivalent support stiffness is obtained by the deformation compatibility at the edge of the corrosion pit. The resulted nonlinear stability equation is solved with a modified iteration method to determine the local critical load. The local critical load for an in-service corroded oil tank roof is analyzed by the proposed approach and the results are compared with those calculated by the conventional nonlinear finite element method with good agreement and the geometrical parameter of the corrosion region corresponding to the minimal critical load is 9.5.