We extend the notion of phase transformations to periodic cellular materials by introducing materials whose unit cells have multiple stable configurations. Each stable configuration of the unit cell corresponds to a stable phase, and transitions between these phases are regarded as phase transformations of the cellular material. We present a cellular material that exhibits phase transformation, identify key elements of the unit cell geometry that yield its mechanical behavior and introduce an analytical model that describes its constitutive behavior. Cellular materials that exhibit phase transformations show hysteresis and their response is characterized by a long serrated loading and unloading plateaus, making these materials attractive for energy absorption applications. While these phase transforming cellular materials offer an energy absorption performance that is comparable to metal and polymeric honeycombs, the key difference is that the deformation on these materials is fully recoverable.