The structure and motion of elephant limbs are unusual compared with those of other animals. Elephants stand and move with straighter limbs (at least when walking), and have limited speed and gait. We devised novel experiments to examine how the limbs of elephants support and propel their mass and to explore the factors that may constrain locomotor performance in these largest of living land animals. We demonstrate that elephant limbs are remarkably compliant even in walking, which maintains low peak forces. Dogma defines elephant limbs as extremely "columnar" for effective weight support, but we demonstrate that limb effective mechanical advantage (EMA) is roughly one-third of that predicted for their size. EMA in elephants is actually smaller than that in horses, which are only one-tenth their mass; it is comparable to human limb values. EMA drops sharply with speed in elephants, as it does in humans. Muscle forces therefore must increase as the limbs become more flexed, and we show how this flexion translates to greater volumes of muscle recruited for locomotion and hence metabolic cost. Surprisingly, elephants use their forelimbs and hindlimbs in similar braking and propulsive roles, not dividing these functions among limbs as was previously assumed or as in other quadrupeds. Thus, their limb function is analogous to four-wheel-drive vehicles. To achieve the observed limb compliance and low peak forces, elephants synchronize their limb dynamics in the vertical direction, but incur considerable mechanical costs from limbs working against each other horizontally.