Research into legged robotics is primarily motivated by the prospects of building machines that are able to navigate in challenging and complex environments that are predominantly non-flat. In this context, control of contact forces is fundamental to ensure stable contacts and equilibrium of the robot. In this paper we propose a planning/control framework for quasi-static walking of quadrupedal robots, implemented for a demanding application in which regulation of ground reaction forces is crucial. Experimental results demonstrate that our 75-kg quadruped robot is able to walk inside two high-slope (50◦) V-shaped walls; an achievement that to the authors’ best knowledge has never been presented before. The robot distributes its weight among the stance legs so as to optimize user-defined criteria. We compute joint torques that result in no foot slippage, fulfillment of the unilateral constraints of the contact forces and minimization of the actuators effort. The presented study is an experimental validation of the effectiveness and robustness of QP-based force distributions methods for quasi-static locomotion on challenging terrain.