High viscosity linear polysiloxane magnetorheological fluid (HVLP MRF) was demonstrated with excellent suspension stability. Such material is suitable for application in the magnetorheological energy absorbers (MREAs) under axial impact loading conditions. On this basis, a new energy absorber incorporating a radial valve with high magnetic field utilization and a corrugated tube is proposed. In energy absorption applications where the MREA is rarely if ever used, our MREA takes the ultra-stable HVLP MRF as controlled medium in order for a long-term stability. For MREA performing at very high shear rates where the minor losses are important contributing factors to damping, a nonlinear analytical model, based on the Herschel-Bulkley flow model (HB model), is developed taking into account the effects of minor losses (called HBM model). The HB model parameters are determined by rheological experiments with a commercial shear rheometer. Then, continuity equation and governing differential equation of the HVLP MRF in radial flow are established. Based on the HB model, the expressions of radial velocity distribution are deduced. The influences of minor losses on pressure drop are analyzed with mean fluid velocities. Further, mechanical behavior of the corrugated tube is investigated via drop test. In order to verify the theoretical methodology, a MREA is fabricated and tested using a high-speed drop tower facility with a 600 kg mass at different drop heights and in various magnetic fields. The experiment results show that the HBM model is capable of well predicting the impact behavior of the proposed MREA.