Acousto-elasticity is concerned with the propagation of small-amplitude waves in deformed solids. Results previously established for the incremental elastodynamics of exact non-linear elasticity are useful for the determination of third- and fourth-order elastic constants, especially in the case of incompressible isotropic soft solids, where the expressions are particularly simple. Specifically, it is simply a matter of expanding the expression for rho upsilon(2), where rho is the mass density and upsilon the wave speed, in terms of the elongation e of a block subject to a uniaxial tension. The analysis shows that in the resulting expression: rho upsilon(2)=a+be+ce(2), say, a depends linearly on mu; b on mu and A; and c on mu, A, and D, the respective second-, third, and fourth-order constants of incompressible elasticity, for bulk shear waves and for surface waves. (C) 2010 Acoustical Society of America. [DOI: 10.1121/1.3372624]