Mechanical components in a robotic system were used to provide body structure and mechanism to achieve physical motions following the commands from electronic controller. This kind of robotic system utilizes complex hardware and firmware for sensing and planning. To reduce computational cost and increase reliability for a robotic system, employing mechanical components to fully or partially take over control tasks is a promising way, which is also referred to as “mechanical intelligence” (MI). This paper proposes a shape memory alloy driven robot capable of using a reciprocating motion to crawl over a surface without any use of electronic controller. A mechanical logic switch is designed to determine the activation timing for a pair of antagonistic shape memory alloy (SMA) actuators. Meanwhile, a compliant pre-strain bistable mechanism is introduced to cooperate with the SMA actuators achieving reliable reciprocating motion between the two stable positions. The SMA actuator is modeled base on a static two-state theory while the bistable mechanism is described by combining a pseudo-rigid-body model (PRBM) with a Bi-beam constraint model (Bi-BCM). Following this, the design parameters of the bistable mechanism and SMA actuators are determined according to theoretical simulations. Finally, a robotic prototype is fabricated using anisotropic friction on its feet to convert the reciprocating motion of the actuator to uni-directional locomotion of the robot body over a surface. Experiments are carried out to validate the presented design concept and the modeling methods.