In this paper, the shock and vibration control effectiveness of the systems based on the magnetorheological (MR) energy absorber (EA) with an internal bypass is investigated and compared with a conventional MREA with an identical volume, the MREA with an internal bypass at passive-on state, and a passive EA based systems. The mechanical model of the single-degree-of-freedom (SDOF) shock and vibration control systems using these four EAs is constructed and the governing equation for the SDOF system is derived. A skyhook control algorithm is used to validate the shock and vibration control performance of the systems. The control performances of the systems under shock loads due to vertical impulses (the maximal initial velocity is as high as 10 m/s) and sinusoidal vibrations are evaluated, compared, and analyzed. The research results indicate that compared to the other three systems, the MREA with an internal bypass based system provides much better vibration control performance, and for the vertical shock control, the MREA with an internal bypass based system requires the shortest settling time to reach steady state and needs shortest travelling stroke.