A computational method is developed for the wave characteristics formulation governing transient nonlinear deformations of locking solids where waves of a moderate unloading process overtake a shocked precursor wave of large uniaxial strain. The unique feature of the proposed all‐event integration scheme is that in order to evaluate the unknowns at a space–time point, not only past events are considered, but also present events surrounding the point in question are accounted for. Moreover, the solution by the proposed method propagates along all existing waves inside a variable space–time grid formed by the bicharacteristic curves associated with the chord‐shock speed of the leading wave (precursor). Based on these features, the method is essentially analytical where in its final stage of development a straightforward numerical integration is required which is free of iteration procedures, stability criteria, and of any other numerical analysis.