This paper reports the concept, design, and development of a pneumatic braided muscle actuator, able to produce bidirectional force and motion. Such a capability can simplify the design and enhance the capabilities of robotic/automation systems using pneumatic muscles as actuators. Finite-element modeling is utilized as a design tool in order to study the feasibility of the concept, where a single braid structure is deformed to produce both contraction and elongation. A three-dimensional finite-element model of the actuator is developed and a number of nonlinear quasi-static simulations are performed using the explicit dynamic solver LS-Dyna to measure the blocked force and free displacement of the actuator. The effect of varying the end-fittings diameter and the length of the inner chamber on the mechanical characteristics of the actuator is also analyzed. The simulation results are validated through mechanical experimentation performed on the functional prototype. With an actuation pressure of 1 bar, the actuator is able to produce a contraction force of around 80 N, extension force of around 40 N, and an overall stroke of >40% of the total length of the actuator. Moreover, the novel actuator has been utilized as a main driver for a one degree of freedom variable stiffness joint, as a case study, to demonstrate the usability of the actuator.