Many walking robot presented in literature stand on rigid flat feet, with a few notable exceptions that embed flexibility in their feet to optimize the energetic cost of walking. This paper proposes a novel adaptive robot foot design, whose main goal is to ease the task of standing and walking on uneven terrains. After explaining the rationale behind our design approach, we present the design of the SoftFoot, a foot able to comply with uneven terrains and to absorb shocks thanks to its intrinsic adaptivity, while still being able to rigidly support the stance, maintaining a rather extended contact surface, and effectively enlarging the equivalent support polygon. The paper introduces the robot design and prototype and presents preliminary validation and comparison versus a rigid flat foot with comparable footprint and sole.