A difference between the isothermal and adiabatic elastic moduli of a crystal signals damping at finite frequencies of vibration. Isothermal and adiabatic elastic moduli of B2 alloys with complete and incomplete long range order are calculated by use of the fluctuation formula of molecular dynamics. The results of the calculation show a decrease of the shear elastic modulus (c(11)-c(12))/2 upon approaching, M-S. This temperature seems to decrease as the long range order decreases. An increase of damping as the temperature is lowered towards M-S is not obtained from the present calculation. (C) 2003 Elsevier Science B.V. All rights reserved.