The single-crystal elastic moduli of natural samples of both calcite (CaCO3) and rhodochrosite (MnCO3) have been measured by Brillouin spectroscopy under ambient condition. Based on the trigonal unit cell, the elastic constants C11, C33, C44, C12, C13, and C14 are 149.4(7), 85.2(18), 34.1(5), 57.9(11), 53.5(9), −20.0(2), and 223.9(15), 132.6(41), 44.5(9), 93.4(21), 76.0(23), −17.3(6) GPa for CaCO3 and MnCO3, respectively. Our data for calcite are in good agreement with earlier data obtained by ultrasonic experiments. The off-diagonal elastic constants (C12, C13, and C14) for rhodochrosite have systematically larger values than the trend defined by other isostructural carbonates, in all of which the divalent cations are alkaline-earth metals. This is a distinctive signature of transition–metal-bearing oxides, which is present in silicates and simple oxides as well.