Abstract: In this parper we present a Fourier pseudospedctral collocation method for boundary imtegral equations of the first kind with a sogarthmec kernel. The diseretr equations are obtained by pseudospectral imterpolation of the symbol assoceated to the integral operator. the cocputations are executed in frequency space by fast fourier travsform. The results show that the numerical accuracy of the pseudospectral collocation cethod are more satisfactry than the Galerkin cillcation ceghod.