Robot feet are crucial for maintaining dynamic stability and propelling the body during walking, especially on uneven terrains. Traditionally, robot feet were mostly designed as flat and stiff pieces of metal, which meets its limitations when the robot is required to step on irregular grounds, e.g. stones. While one could think that adding compliance under such feet would solve the problem, this is not the case. To address this problem, we introduced the SoftFoot, an adaptive foot design that can enhance walking performance over irregular grounds. The proposed design is completely passive and varies its shape and stiffness based on the exerted forces, through a system of pulley, tendons, and springs opportunely placed in the structure. This paper outlines the motivation behind the SoftFoot and describes the theoretical model which led to its final design. The proposed system has been experimentally tested and compared with two analogous conventional feet, a rigid one and a compliant one, with similar footprints and soles. The experimental validation focuses on the analysis of the standing performance, measured in terms of the equivalent support surface extension and the compensatory ankle angle, and the rejection of impulsive forces, which is important in events such as stepping on unforeseen obstacles. Results show that the SoftFoot has the largest equivalent support surface when standing on obstacles, and absorbs impulsive loads in a way almost as good as a compliant foot.