Elastic constant measurements have been made on a single crystal of palladium in the temperature range 4.2-300°K. Extrapolation of the data to absolute zero gives c11=2.341+/-0.027×1012 dyne cm-2, c12=1.761+/-0.027×1012 dyne cm-2, c44=0.712+/-0.003×1012 dyne cm-2. The corresponding value of Debye temperature is θ0=275+/-8°K, which compares well with the calorimetric figure of θ0=274+/-3°K. Both shear constants show an anomalous temperature dependence. This dependence can be correlated with the temperature variation of the contribution to C=c44 and C'=12(c11-c12), resulting from the presence of holes in the d band of palladium.