The article addresses mathematical aspects concerning the computation of spatial flow around lifting surfaces in supersonic regimes utilizing the discrete vortex method. The study outlines the problem formulation and boundary conditions for the wave equation, and justifies the application of discrete vortex elements in these calculations. Analytical expressions for determining the disturbed velocity at flow points induced by vortex segments are presented, along with a discussion on the method’s application in the presence of shock waves. The results confirm that the discrete vortex method is a viable tool for tackling supersonic aerodynamic problems, including nonlinear complexities.