9Omphacite, a clinopyroxene mineral with two distinct crystallographic sites, M1 and M2, and 10 composition intermediate between diopside and jadeite, is abundant throughout the Earth's upper 11 mantle, and is the dominant mineral in subducted oceanic crust. Unlike the end-members, 12 omphacite exists in two distinct phases, a P2/n ordered phase at low temperature and a high-13 temperature C2/c disordered phase. The crystal structure and full elastic constants tensor of ordered 14 P2/n omphacite have been calculated to 15 GPa using plane-wave density functional theory. Our 15 results show that several of the elastic constants, notably C 11 , C 12 , and C 13 deviate from linear-16 mixing between diopside and jadeite. The anisotropy of omphacite decreases with increasing 17 pressure and, at 10 GPa, is lower than that of either diopside or jadeite. The effect of cation disorder 18 is investigated through force-field calculations of the elastic constants of Special Quasirandom 19 2 Structures supercells with simulated disorder over the M2 sites only, and over both cation sites. 20These show that cation order influences the elasticity, with some components displaying particular 21 sensitivity to order on a specific cation site. C 11 , C 12 , and C 66 are sensitive to disorder on M1, while 22 C 22 is softened substantially by disorder on M2, but insensitive to disorder on M1. This shows that 23 the elasticity of omphacite is sensitive to the degree of disorder, and hence the temperature. We 24 expect these results to be relevant to other minerals with order-disorder phase transitions, implying 25 that care must be taken when considering the effects of composition on seismic anisotropy. 26