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The first pressure derivatives fo the elastic moduli for three austenitic stainless steels, AISI 304, 310, and 316, have been determined from the variation of the sound velocity under pressure. All pressure derivatives are lower than the corresponding ones for pure iron. The elastic Grüneisen constant, derived from the pressure derivatives is somewhat lower than the corresponding thermodynamic constant. The decrease in the elastic moduli and their pressure derivatives with respect to the corresponding values for pure iron is correlated with the alloying content of nickel and chromium.