The double-Mach reflection (DMR) of oblique shock waves in pseudo-stationary flows has been investigated. The equations of motion of the first and second triple point were formulated, as well as the relative motion between these two triple points. The equation of motion for each triple point consists of 14 nonlinear algebraic equations. An analytical method of solution is presented. Consequently, for the first time a complete analytical solution of a DMR is given. Utilizing this analytical solution a method for predicting the second triple-point trajectory angle is developed. The analytical results are compared with experiments that were performed on the 10 × 18 cm Hypervelocity Shock Tube at the University of Toronto Institute for Aeronautical Studies. Good agreement was obtained.