The Boltzmann‐Ehrenfest principle of adiabatic invariance is applied to a nonlinear system consisting of a self‐constrained finite amplitude acoustic wave propagating in a solid. The results predict the existence of an acoustic radiation stress having two source components. One component is associated with the stress nonlinearity of the solid and is obtained from the adiabatic variation in a parametrized natural wave velocity. The second component results from the variation in the first‐order nonlinear term in the virial theorem expansion and gives rise to an acoustic radiation‐induced static strain. Both components depend directly on the energy density of the propagating wave but are opposite in sign. The coefficient which couples the radiation‐induced static strain to the energy density is the acoustic nonlinearity parameter which characterizes the nonlinearity of the wave equation.