The non‐reactive OPLS‐AA force‐field is used to compare direct shock and Hugoniostat simulations of a melt of cis‐1,4‐polybutadiene at different shock velocities and with chain lengths up to 500 monomers. Both methods yield equivalent Hugoniot data with negligible influence of the chain length. However, it is found that the dynamical compression effects induce a time‐dependent anisotropy in the stress tensor in the direct shock simulations, yielding a non‐zero shear component. This anisotropy vanishes to the usual isotropic stress through two specific relaxation mechanisms: a fast process (characteristic time ≈1 ps) associated with the relaxation of the local intramolecular degrees of freedom of the chains, and a second slower process (characteristic time ≈100 ps) associated with the structural reorganisation of the polymer chains, involving long‐range intramolecular and intermolecular interactions. A third potential relaxation process, associated with entanglements, may be at play but is beyond the scope of the present study.