A modified version of the method of strained coordinates is introduced which allows to circumvent the solution of a weakly nonlinear, hyperbolic wave equation by solutions of linear equations. The method is then applied to the analytic description of unsteady reflection of weak shock waves. Here we are especially interested in improving our understanding of the transition from regular reflection to Mach‐reflection which until now has not been dealt with adequately in the literature (von‐Neumann‐paradox).