This paper discusses the disturbance velocity and potential as well as the total velocity formulation for non lifting potential flow problem. The problem is derived based on the Cauchy method formulation. The adding and subtracting back technique is used to desingularize the integral equations. The desingularized boundary integral equations are then discretized. The discretized equations can be evaluated using an arbitrary high order Gaussian quadrature or any other numerical integration method. Numerical examples for ellipse and Joukowski airfoil are calculated and compared with the analytical solution. It is shown that the usage of a desingularized Cauchy's formula in potential flow computation leads to an efficient and an accurate determination of the velocity and pressure on the body surface.