The object of this study is measurement of a stress and the reliable third order elastic constants of the engineering material using the original theory and the measurement of elastic wave propagating velocity. The change of elastic wave propagating velocity caused by applied stress was measured for the specimen cut off from semi-continuous casting ingot of A3004 aluminum alloy. From the point of view of Lagrangian description where state before deformation was used as the reference coordinate, Murnaghan's third order elastic constants could be obtained by use of the changing ratio of elastic wave velocity under applied stress, stress-strain relation, and the equation of stress dependence on elastic wave velocity. As a result, authors found a new method of stress measurement by introducing the stress dependent coefficients to elastic wave velocity.