Primates exhibit unusual quadrupedal features (e.g. diagonal gaits, compliant walk) compared with other quadrupedal mammals. Their origin and diversification in arboreal habitats have certainly shaped the mechanics of their walking pattern to meet the functional requirements necessary for balance control in unstable and discontinuous environments. In turn, the requirements for mechanical stability probably conflict with mechanical energy exchange. In order to investigate these aspects, we conducted an integrative study on quadrupedal walking in the olive baboon (Papio anubis) at the Primatology station of the CNRS in France. Based on kinematics, we describe the centre of mass mechanics of the normal quadrupedal gait performed on the ground, as well as in different gait and substrate contexts. In addition, we studied the muscular activity of six hindlimb muscles using non-invasive surface probes. Our results show that baboons can rely on an inverted pendulum-like exchange of energy (57% on average, with a maximal observed value of 84%) when walking slowly (<0.9 m s−1) with a tight limb phase (∼55%) on the ground using diagonal sequence gaits. In this context, the muscular activity is similar to that of other quadrupedal mammals, thus reflecting the primary functions of the muscles for limb movement and support. In contrast, walking on a suspended branch generates kinematic and muscular adjustments to ensure better control and to maintain stability. Finally, walking using the lateral sequence gait increases muscular effort and reduces the potential for high recovery rates. The present exploratory study thus supports the assumption that primates are able to make use of an inverted pendulum mechanism on the ground using a diagonal walking gait, yet a different footfall pattern and substrate appear to influence muscular effort and efficiency.