Semi-active shock and vibration isolation systems using magnetorheological energy absorbers (MREAs) require minimization of the field-off damping force at high speed. This is because the viscous damping force for high shaft speed become excessive. This implies that the controllable dynamic force range, defined as the ratio of the field-on damping force to the field-off damping force, is dramatically reduced. In addition, fail-safe MREA performance, if power were to be lost, is of great importance to shock and vibration isolation systems. A key design goal is to minimize field-off damping force while maximizing MREA dynamic force, while maintaining fail-safe performance. This study presents the principle of a bidirectional-controllable MREA that can produce large damping force and dynamic force range, as well as excellent fail-safe performance. The bidirectional-controllable MREA is configured and its hydro-mechanical model is theoretically constructed. From the hydro-mechanical model, the mathematical model for the MREA is established using a Bingham-plastic nonlinear fluid model. The characteristics of the MREA are theoretically evaluated and compared with those of a conventional flow-mode MREA with an identical volume. In order to investigate the feasibility and capability of the bidirectional-controllable MREA in the context of the semi-active shock and vibration isolation systems, a mechanical model of a single-degree-of-freedom (SDOF) isolation system using a bidirectional-controllable MREA is constructed and the governing equation for the SDOF isolation system is derived. A skyhook control algorithm is utilized to improve the shock and vibration isolation performance of the isolation systems. Simulated vibration isolation performance using bidirectional-controllable and conventional MREAs under shock loads due to vertical impulses (the initial velocity is as high as 10 m/s), and sinusoidal vibrations, are evaluated, compared, and analyzed.