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A relaxation procedure has been developed to treat the three-dimensional, transonic small-perturbation equations about finite lifting wings. A combination of two schemes is employed. For flow forward of the wing trailing edge the equations are written in terms of a velocity potential in order to minimize computer algebra and storage. For the remaining flowfield the equations are written in terms of the velocity components in order to simplify the enforcement of the Kutta condition. Difference equations and relaxation procedures are described for both schemes. The computational method automatically captures the embedded shock wave in the three-dimensional flowfield. Computed results agree with other inviscid methods and experiment.