A method employed heretofore by the authors to obtain approximate solutions of the transonic flow equation for plane and axisymmetric flow is extended to give reasonable results for wings of finite span, consistent with the known properties of transonic flows. In this method the partial differential equation appropriate to the study of transonic flow is replaced by a nonlinear ordinary differential equation which can be solved by numerical methods. Asymptotic forms of this differential equation are given for very high and very low aspect ratios and analytic results are obtained for certain special cases. Numerical results, calculated by use of electronic computing machines, are given in the form of pressure distribution and pressure drag for two profile shapes, wedge and circular arc, for wings of rectangular plan form. The range of aspect ratios covered extends effectively from zero to infinity and agreement with the asymptotic results is shown at both limits.