Abstract: A transonic axisymmetrical potential equation with large disturbance in the free stream direction and small disturbance in the transverse direction is solved by using the Murman-Cole schemes of finite differences.The boundary condition on the body is transfered to body axis.The boundary condition at farfield is approximated by that at infinite.Finite difference equations for the potential are solved by line-overrela-xation along the radius with Seidel iteration.In order to calculate the pre-ssure on the body surface,the potential is interpolated by the slender-body theory.The pressure coefficient is calculated by the exact Bernoulli's equation.The zero-lift wave-drag coefficients are obtained by integrating the pressure coefficients on the body surface.The computational results for seven different configurations agree well with the known wind tunnel test data as shown In Fig.2 to Fig.6.The experiences obtained from investigation of mesh spacings,initial-fields,iterative methods,relaxation factors etc.in relation to the convergence and convergent rate may be interesting to engineers.A linearized analysis of the stability and the convergence in line overrelaxation of difference equations for steady axisymmetric small perturbation potential flow is carried out and the conclusions are shown in table 1.The numerical computations do agree with the theoretical conclusions.It must be pointed out that as M∞ is very close to unit or the mesh spacing is shortened,the iterative computation does not converge to the usual degree of accuracy.This fact might be explained by vanishing of the artificial viscosity in the potential difference equation at locally supersonic points.