Third order elasticity theory may be used to show that a longitudinal acoustic wave normally incident on a sample in a state of plane deformation experiences a relative velocity shift given by [equation] where B is the acoustoelastic constant, σ₁ and σ₂ are the principal stresses normal to the direction of wave propagation, and V₀ is the wave velocity in undistorted material. Hence, wave transit time measurements may be used to ascertain the sum σ₁ + σ₂ in the deformed state. We use a double pulse-echo technique to provide an accurate measure of transit time through the thickness of aluminum discs produced by hydrostatic extrusion (25% area reduction). The residual stress state produced during extrusion is axi-symmetric and we are able to separately determine residual radial and hoop stresses by a single longitudinal wave measurement at points on the disc face. The technique is extremely rapid and accurate, and the acoustic results are cross-checked by both x-ray measurements and finite element simulation of the extrusion process.