The objective of the work is related to the modelling of micro-cavities replication in polymer plates by the roll embossing process. Finite element simulations are set up and performed to analyse the polymer deformation and flow leading to the filling of micro-cavities engraved on the moving roll system in the roll to roll (R2R) process. In the proposed approach, the roll engraved with micro-cavities is assumed to be undeformable, whereas the polymer plate rigid exhibits a viscoelastic or a coupled viscoelastic-viscoplastic material behaviour depending on the experimental processing conditions. The flow behaviour of the selected materials (cyclic olefin copolymer, COC) depends on the experimental processing parameters (rolling velocity, applied pressure and temperature) that are considered. The numerical simulations are performed using LsDyna® finite element software in order to analyse the filling of the microcavities vs. the rolling velocity and temperature, as a function of friction and sliding conditions. The results lead to the choice of roll embossing conditions in order to get the micro-cavities with the required geometries and properties.