The details of Theodorsen's method for computing the conformal map from the ex- terior of the unit disk to the exterior of a simple closed curve in the complex plane are reviewed. An implementation of the method in Matlab is presented and used to compute potential ow over a single airfoil. Pressure curves and circulations for ows satisfying the Kutta condition at the trailing edge of the airfoil are calculated and the results are compared to output from a standard engineering code.