The paper defines generalized similarity solutions for the case of a three-dimensional laminar compressible boundary layer on a swept swept wing in a supersonic flow. For this purpose, an infinitely elongated sliding cylinder with a profile-shaped section is studied as a physical model. In this case, it is assumed that in the considered range of running Mach numbers $(1\leq M_\infty\leq5)$ the assumptions about the ideal state of the flowing gas and the linear dependence of the dynamic viscosity on temperature are still admissible. The universal mathematical model of the problem under consideration, obtained as a result of three successive transformations (Stuartson, Salnikov’s generalized similarity [2] and a set of parameters of Loytsyaisky’s generalized similarity [7]) of the corresponding initial system of equations, is solved numerically on the ECCM, using the difference iterative method of simple sweep, for various options for the following values of freely accepted parameters: $\mathrm{Pr}=0,72$, $M_\infty=1;3;5$, sliding angle $\beta=0^\circ;20^\circ;40^\circ$, dimensionless temperature on the wall $T_w/T_0=0.50;0.98;1.20$ and the compressibility parameter in the direction of the aerodynamic chord $f_{0x}=0.5;0.95$. From the numerous calculated results, several interesting distributions of the characteristic values of the boundary layer over which the analysis is performed are selected and graphically presented.