As a rare metal material with low density, high strength and high melting point, beryllium (Be) is widely utilized in many fields including aerospace and vehicles. Dynamic loadings such as impact and high-rate compression often happen in the applications of Be materials in these fields. However, the dynamic behaviors of Be materials under high pressure and high-rate loading have not been fully investigated, although they are valuable for better applications of Be materials. articularly, the effect of twinning on dynamic behaviors of Be material is very important for better understanding the plasticity deformation mechanism of Be material. In this paper, a thermoelastic-viscoplastic crystal plasticity model is developed for dynamic behaviors of Be material under high pressure and high strain-rate loading based on the physical mechanism of plasticity deformation. Besides, the dislocation motion and work hardening are considered within the constitutive framework by the Orowan relation and the Taylor equation respectively, and the contribution of twinning to the plasticity deformation is also considered via twinning fraction evolution and fragmentation of crystal due to twinning deformation. With the model, dynamic behaviors of Be material are investigated, including effect of pressure on the dynamic yield strength, the quasi-elastic unloading behavior, and evolution of twinning in shock loading and unloading. Compared with the classical SG model, the model developed in this paper accords better with the experimental results in predicting yield strength of Be material under impact loading, especially with high pressure. Moreover, it is revealed that the condition of yield strength of the Be material is divided into three cases, namely the non-twinning under low pressure, the twinning deformation under moderate pressure, and the twinning fragmentation under high pressure. The unloading behavior of Be material under impact loading is also studied with the model, and the quasi-elastic unloading behavior observed in experiments many times, is faithfully predicted. It is found that the quasi-elastic unloading phenomenon of the material is closely related to the variation of the shear velocity of shock wave with the shear strain, which suggests that the non-linear elastic property of the material is an important reason for this phenomenon. Finally, the evolution of twinning of Be material in the shock loading is studied, showing that the increasing of twinning friction happens not only in the loading process but also in the unloading process of the shock waves. Some crystals break up into sub-crystals due to the fact that the volume fraction of twinning exceeds the critical fraction in the evolution of twinning.