The elastic constants and Pockels coefficients of CH4 and CD4 single crystals near their triple points have been determined using high-resolution Brillouin spectroscopy. For CH4 at 90.4 K, the elastic constants are C11 = 19.57 ± 0.30, C12 = 14.46 ± 0.20, C44 = 9.20 ± 0.15 kbar, and the ratios of the Pockels coefficients are p12/p11 = 1.031 ± 0.035 and p44/p11 = 0.069 ± 0.010. For CD4 at 89.2 K, C12 = 20.04 ± 0.30, C12 = 15.00 ± 0.25, C44 = 9.15 ± 0.15 kbar, and p12/p11 = 1.027 ± 0.020, P44/p11 = 0.138 ± 0.010. The velocities of the low-frequency transverse modes in CH4 and CD4 are anomalously slow in the [Formula: see text] direction, indicative of rotational–translational coupling of molecules. Isotopic differences are also evident: the Pockels coefficient p44 in CD4 is double that in CH4; and the velocities of both transverse modes in the principle directions [Formula: see text], [Formula: see text], and [Formula: see text] are in the ratio V(CH4)/V(CD4) = 1.130 instead of 1.118 as expected from the isotopic mass ratio.