In this paper we seek refined yet efficient computational models of large overall motion in statics and dynamics. The efficiency is achieved by the proposed model of 8-node brick element with rotational degrees of freedom which allows to separate large displacements and large rotations. The independent rotation field leads to an intrinsic representation of the rotation tensor, ensuring a smooth interaction between 3D solids and beam elements. The element is based on a sound variational formulation and the incompatible mode method which allows to construct enhanced strain representation. Several numerical examples are presented to show an excellent performance of this element in the whole range of large overall motion in the statics and dynamics problems.