The scattering properties of a periodic array of conductors having any shape, composed of steps along the coordinate axes, and illuminated by a plane wave, are obtained through a rooftop current approximation. The solution, which involves a finite-dimension matrix equation, is described along with an algorithm that efficiently generates the matrix elements. Results presented for arrays of rectangular apertures and thin, rectangular plates are shown to closely agree with those obtained through standard modal approaches. Convergence with respect to the number of current elements is also explored. Because the normal component of the edge current is nonzero and continuous when thickness is present, convergence is significantly better than for zero-thickness structures. At glancing incidence, however, accuracy requires a finer subsection grid to properly represent the circulating current on the sidewalls for plates, and the U-shaped current flowing near the corner of the sidewalls for apertures.