Part III deals with the nonlinear transient response of an elastic‐plastic locking half‐space traversed by converging waves of uniaxial large strain generated as a result of a uniform loading–unloading blast suddenly applied with no rise time to the entire surface of the half‐space. For this type of boundary‐value problem where a shocked leading wave interacts continuously with faster overtaking unloading waves, a computational method was developed based on the theory of characteristics. This method, which employs an all‐events integration process propagating along the existing wavelets, is essentially analytical. In its final stage of the solution, a straightforward numerical integration is required free of iteration procedures, stability criteria, and any other numerical analysis. The resultant response of the half‐space is described and interpreted here.