In waste heat recovery applications, thermoelectric (TE) generators are subjected to thermal gradients and thermal transients, creating mechanical stresses in the TE legs. Such stresses are functions of the elastic moduli of the TE material. For SnTe1 +/- x matrices (where x = 0.0 or 0.016) composite specimens with 0-4 vol% SiC nanoparticle (SiCNP) additions, the elastic moduli (Young's modulus, shear modulus, and Poisson's ratio) were measured by resonant ultrasound spectroscopy from room temperature (RT) to 663 K. The effects of matrix composition and the SiCNP additions on the RT intercepts and the slopes of the elastic modulus as a function of temperature are also discussed.