This paper is concerned with the finite element analysis of electromagnetic scattering from an axially symmetric perfectly conducting body of revolution with an arbitrary cross section in free space. The coupled azimuthal potential formulation is used to express the solution in terms of the two field components, Eф and Hф. The use of a Fourier series expansion reduces the three-dimensional problem to a series of two dimensional problems. At the truncation boundary the measured equation of invariance (MEI) is used. The MEI method uses information about the scatterer to find an equation for the boundary nodal values in terms of the values at neighboring nodes. The MEI produces a boundary condition which allows the matrix to retain its sparse structure. This method also allows the finite element mesh to be truncated very close to the body. Numerical examples are given for spheres, finite cylinders, and a cone.