Atomistic simulations were used to calculate the isothermal elastic properties for beta-, alpha-, and delta-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX). The room-temperature isotherm for each polymorph was computed in the pressure interval 0less than or equal topless than or equal to10.6 GPa and was used to extract the initial isothermal bulk modulus K-o and its pressure derivative using equations of state employed previously in experimental studies of the beta-HMX isotherm. The complete elastic tensor for each polymorph was calculated at room temperature and atmospheric pressure. For the case of beta-HMX, the calculated elastic tensor is compared to one based on a fit to sound speed data yielding reasonably good agreement. The bulk modulus of beta-HMX obtained from equation-of-state fits to the room-temperature isotherm agrees well with that determined from the complete elastic tensor and from volume fluctuations at atmospheric pressure. However, the value of K-o obtained from the isotherm is sensitive to choice of equation of state fitting form and to the weighting scheme employed in the fit. Based upon simulation results and reanalysis of experimental data, the commonly accepted value of the initial isothermal bulk modulus for beta-HMX should be revised from a value of similar to12.4-13.5 GPa to similar to15-16 GPa. The present report provides the first accurate determination of the elastic tensors and isotropic moduli for alpha- and delta-HMX. Predicted values of the shear moduli for alpha- and delta-HMX are more than a factor of 2 smaller than for beta-HMX. (C) 2003 American Institute of Physics.