A multi-dimensional discrete Fourier series method has been developed to calculate the coupling capacitances in VLSI circuits. In the present method a scalar potential Φ(r) is generated, in discrete Fourier series form, which is related to the known electric potential distributions by Laplace equation. By using the multiple radix Fast Fourier Transform (FFT) algorithm to reduce the CPU time, the electric field strength can be obtained from the gradient of the scalar potential. The calculated 2-D and 3-D results generally compare well with the conventional approach results. A program has been developed and numerical results are discussed. © 1989.