In this paper, we investigate the energetics of constant height level bounding gaits in quadruped robots with asymmetric body-mass distribution along the longitudinal axis. Analytical expressions for mechanical specific resistance for two cases of bounding are derived: bounding with equal front and rear leg step lengths, and bounding with unequal front and rear leg step lengths. Specific resistance is found to be independent of mass distribution in the first case, and dependent in the second case. The quadruped robot has average nonzero acceleration/deceleration due to unsymmetric distribution of mass when front and rear leg step lengths are equal. Results show that lower body lengths, lower step lengths, and higher heights from the ground level give lower specific resistance. The effect of body-mass asymmetry is to accelerate in the first case, and to reduce specific resistance in the second case. This result provides some insight into why certain quadrupedal animals in nature evolved to have body-mass asymmetry. © 2014 Cambridge University Press.