Biological muscle is a multifunctional actuator capable of varying its stiffness and damping. The design of similarly multipurpose variable impedance actuators has benefits for improving physical robot interaction, such as by enabling variable impedance manipulators with more capability and greater safety. We present the concept for a soft jamming brake and artificial muscle (SJBAM). By incorporating a jamming brake inside of a pneumatic artificial muscle, we achieve synergistic benefits, which enable new functionalities, improve muscle static and dynamic response, and expand the brake’s capabilities. The SJBAM can store elastic energy, such as a pneumatic artificial muscle, and also act as a brake or clutch. By independently controlling the muscle and brake pressures, we can vary the SJBAM’s stiffness and damping. We derive models for this actuation concept and examine the performance of the SJBAM both theoretically and experimentally. In addition, we present open- and closed-loop position control demonstrations with a 1-degree-of-freedom manipulator actuated by an antagonistic pair of SJBAMs.