In this paper, an efficient method is developed to model the scattering of electromagnetic waves by large three-dimensional perfectly conducting (PEC) bodies of revolution with sharp edges. The magnetic field integral equation (MFIE) is implemented and applied to a finite solid cylinder, including the upper and lower end caps. Point matching is used to construct the interaction matrix. The numerical instabilities that generally occur to the current behavior near sharp edges are completely eliminated by the proper choice of special base functions near the edges. Not taking the singular behavior of the currents into account leads to a bad convergence or to incorrect results.