Tendon elasticity is important for economical locomotion; however it is unknown whether tendon stiffness is appropriate to achieve an optimal efficiency in various muscles. Here we test the hypothesis that the Achilles tendon is of an appropriate stiffness to maximise medial gastrocnemius muscle efficiency during locomotion with different power requirements. To test this hypothesis we used a three element Hill muscle model to determine how muscle fascicles would be required to change length if the series elastic element stiffness is varied, whilst the limb kinematics and muscle properties are held constant. We applied a model of muscle energetics to these data to predict muscle efficiency for a range of stiffness values in both walking and running conditions. We also compared the model results to in vivo data collected using ultrasonography. The muscle model predicted that optimal series elastic element stiffness for maximising efficiency is equal or slightly higher than that of the average Achilles tendon in running and walking, respectively. Although the peak efficiency values for running (26%) and walking (27%) are similar, the range of stiffness values achieving high efficiency in running is much smaller than that during walking. These results suggest that a compliant tendon, such as the Achilles tendon, is required for efficient running. Such a finding is important, because it describes how the stiffness of a tendon may be adapted to achieve optimal efficiency for particular athletic pursuits. The influence of varying tendon stiffness on kinematic performance may, however, play an important role in determining the efficiency of the muscle.