Abstract Bistable soft robots are gaining momentum for their fast speed. This study presents a novel asymmetric mechanically prestressed, pneumatically driven, bistable laminated soft actuator. Its two orthogonal stable shapes are created by prestretching two orthogonal elastomer matrix composites before bonding them to a thin core layer. Two fluidic layers with fluid channels are bonded on either side of the core layer to actuate and trigger the snap-through process of the actuator. An analytical model is proposed as follows: the actuator net energy is calculated based on polynomials with unknown coefficients, and the stable shapes of the actuator are computed as a result of pneumatic pressure and external loads with the Rayleigh–Ritz method. Bistable actuators are fabricated with different prestrains, and motion capture and tensile loading experiments are conducted for model validation. A gripper is fabricated with two bistable actuators and demonstrated to grasp a variety of objects. Sensitivity studies are performed to identify the actuator response as a function of a variety of design parameters.