The diffraction problem of a plane shock wave at the apex of an obtuse wedge treated by Lighthill (1950) is extended by assuming that the shock wave strikes the walls of the obtuse wedge at some finite oblique angle of incidence (not exceeding the critical angle). Transformations similar to that performed in the above-mentioned paper lead to a non-symmetrical boundary-value problem for an analytic function of a complex variable having a non-homogeneity in the form of a delta-function. It was found possible to extend, for the case considered, the method developed by Lighthill and construct the solution in almost as simple a form as given in the above-mentioned paper. The case of three-dimensional stationary flow is considered when the line of reflexion makes a finite angle with the edge of the wedge.