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The velocities of the ultrasonic bulk waves propagating in a prestressed material with orthorhombic symmetry are formulated in two frames of reference. From these velocities, acoustoelastic coefficients are theoretically determined with the natural and initial coordinates. For each acoustoelastic coefficient, the differences between its expressions according to the two systems of coordinates are then theoretically calculated and experimentally determined. From these results, the error on the residual stress evaluation due to the use of natural acoustoelastic coefficients rather than those defined with the initial coordinates is estimated. © 1999 American Institute of Physics.