A scalar field diffracted by a rigid rectangular plate can be computed with the formula that Otsuki derived by applying the properties of Weber–Schafheitlin’s discontinuous integral (also referred to as the Kobayashi potential). This method may be regarded as giving an eigenfunction expansion of the wave functions of the present configuration, although these functions are expressed by double infinite integrals. Expansion coefficients are determined from the matrix equations, and the matrix elements are given by double infinite integrals. An algorithm effective for computing these integrals is developed here by using the asymptotic expansions for the integrands. As a result, the original integral reduces to a finite double integral plus two finite single integrals. The numerical results for some diffraction patterns are presented. With relatively large plates, the results agree well with those obtained from the Kirchhoff diffraction integral. ©1997 American Institute of Physics.