This paper presents a new planar flexure-based bistable two-jaw parallel gripper mechanism. The bistability of the mechanism is enabled by a pinned-pinned buckled beam suspended onto two cross-spring pivots. External energy is required only during the switching between the two stable states: open and closed jaws. This is particularly advantageous in gripping applications where power consumption is a limiting factor. Since it is based exclusively on flexure elements, this gripper mechanism is free from friction, wear and lubricant and is well suited for cleanroom environments, biomedical applications, or space environments. Another key feature is that the jaw opening/closing motion is based on fast snap-through transitions of the buckled beam, relying on an actuator motion which can be comparatively slow. This is highly beneficial for high-speed pick-and-place applications. Furthermore, the elastic decoupling between the actuator and the jaws allows the gripper to safely apply a limited output force to the grasped object, regardless of the force supplied by the actuator. In this article, the nonlinear load-deformation behaviors of the gripper are analytically modeled using Euler-Bernoulli beam theory and validated using finite element modeling. A prototype of the gripper mechanism with an external size of 10 mm x 35 mm x 85 mm was monolithically manufactured out of steel using wire electrical discharge machining. A voice coil actuator is integrated for actuation. The load-deformation characteristics, as well as the time to switch state, were measured on the prototype using a dedicated testbed. The experimental data are in good agreement with the theoretical models. The results show a stable gripping force of 1 N, a maximum stroke per jaw of 1.7 mm, and a state switching time (i.e., snap-through time) below 7 ms demonstrating high-speed gripping performances in comparison to state-of-the-art grippers.