Publisher Summary This chapter discusses hierarchical approach to flow calculations for polymeric liquid crystals. Starting from an atomistically detailed description of the LC-forming poly-n propyl isocyanate) PPIC, a sequence of coarse-graining steps have been performed in order to obtain a macroscopic description of a PPIC solution in toluene which can be employed in viscoelastic flow calculations. The two first levels of description reside at the atomistic level and differ only in a computationally convenient reduction of the number of degrees of freedom through the introduction of holonomic constraints. Level 1 are reduced to only two mesoscopic parameters describing the rotary diffusivity of PPIC helices (considered as rigid rods) and the entropic excluded volume interaction between rods via purely geometric parameters and not in a fully thermodynamically consistent way. Finally, the use of a model reduction technique was demonstrated by integrating the Fokker-Planck equation, which controls the dynamic evolution along a streamline for which the history of the strain rate had been calculated with CONNFFESSIT.