The pressure dependences of the second-order elastic constants C-ij and the velocity of sound in 3C-SiC and 2H-SiC crystals are calculated in the framework of the Keating model with the additional assumption that the central α and the noncentral β force constants are linear functions of external hydrostatic pressure. Gruneisen parameters for the different acoustic modes of 3C-SiC have been also calculated. The third-order elastic constants C-ijk for 3C-SiC are determined from the dependences of C-ij on the pressure.