Experimental data on the propagation of shear waves in annealed aluminum subjected to biaxial prestresses in the plastic range are presented. In addition, experimental evidence of the catastrophic straining at one “point” in a specimen while other “points” are not affected is given for annealed aluminum. Such evidence is not consistent with the material possessing a smooth stress-strain relation, but is compatible with the stair-case type of response. A shock wave theory which is a generalization of our previous work to the case of a biaxial prestress is also described. This theory is applied to the experimentally determined staircase stress-strain relation for aluminum. The same stress-strain relation is used for a wide range of strain rates and predicts a variety of wave speeds which are shown to be consistent with the experimental data. It is found that the biaxial prestress does not lead to any new phenomena but does modify some specific values. Some illustrative boundary-value problems are also discussed.