This paper introduces a new method for constructing approximate solutions to a class of Wiener{Hopf equations. This is particularly useful since exact solutions of this class of Wiener{Hopf equations, at the moment, cannot be obtained. The proposed method could be considered as a generalisation of the \pole removal" technique and Schwarzschild's series. The criteria for convergence is proved. The error in the approximation is explicitly estimated, and by a su cient number of iterations could be made arbitrary small. Typically only a few iterations are required for practical purposes. The theory is illustrated by numerical examples that demonstrate the advantages of the proposed procedure. This method was motivated by and successfully applied to problems in acoustics. 1.