The three elastic constants of tantalum, tungsten, and molybdenum have been measured in the temperature range between 4.2 and 300°K. The directly measured quantities CL and 12(C11-C12) for molybdenum and the computed bulk moduli of all three elements show an anomalous temperature dependence. These data along with published results for other metals generally show a difference in temperature dependence of the bulk modulus between 3d and 4d-5d metals. Overlap contributions to the elastic constants are found to favor an antiferromagnetic ordering. The Debye characteristic temperatures calculated from elastic constants are found to be in substantial agreement with results obtained from calorimetry.