We measure the full elastic tensors of Mn3Ge and Mn3Sn as a function of temperature through their respective antiferromagnetic phase transitions. Large discontinuities in the bulk moduli at the Néel transitions indicate strong magnetoelastic coupling in both compounds. Strikingly, the discontinuities are nearly a factor of 10 larger in Mn3Ge than in Mn3Sn. We use the magnitudes of the discontinuities to calculate the pressure derivatives of the Néel temperature, which are 39 K/GPa 14.3 K/GPa for Mn3Ge and Mn3Sn, respectively. We measured the in-plane shear modulus c66, which couples strongly to the magnetic order, in magnetic fields up to 18 T and found quantitatively similar behavior in both compounds. Recent measurements have demonstrated strong piezomagnetism in Mn3Sn: Our results suggest that Mn3Ge may be an even better candidate for this effect. © 2022 American Physical Society.