Various static and (equilibrium and non-equilibrium) dynamic molecular-level computational methods and tools are utilized in order to investigate the basic shock-wave physics and shock-wave material interactions in polyurea (a nano-phase segregated elastomeric co-polymer). The main goal of this investigation was to establish relationships between the nano-segregated polyurea microstructure (consisting of rod-shaped, discrete, so-called "hard domains" embedded into a highly compliant, so-called soft matrix) and the experimentally established superior capability of this material to disperse and attenuate resident shock waves (e.g., those generated as a result of blast-wave impact). By analyzing molecular-level interactions of the shock waves with polyurea, an attempt was made to identify and quantify main phenomena and viscous/inelastic deformation and microstructure-altering processes taking place at the shock front, which are most likely responsible for the superior shock-mitigation behavior of polyurea. Direct molecular-level simulations of shock-wave generation and propagation in the "strong-shock" regime are utilized in order to construct the appropriate shock-Hugoniot relations (relations which are used in the construction of the associated continuum-level material models). Extension of these relations into the "weak-shock" regime of interest from the traumatic brain injury prevention point of view is also discussed.