The scattering problem of a perfectly conducting rectangular box illuminated by a linearly polarized electromagnetic plane wave is numerically solved through consideration of the vector magnetic field integral equation. Because the scattering obstacle is three‐dimensional and possesses no rotational symmetry, the vector integral equations consist of coupled scalar integral equations, which are reduced by the method of moments. Numerical results are presented for broadside incidence where symmetry arguments are used to produce an eightfold reduction in matrix size. Calculated currents and radar cross sections for a square plate and a cube show good agreement with measurements found in the literature. Techniques for analyzing the case of arbitrary incidence are also included.