The micro hot-embossing process is an efficient and low-cost manufacturing process that can produce components with complex geometries in a wide variety of materials. The physical behaviour of the material needs to be investigated to achieve optimisation of the process. Many experimental results have been presented in the literature; however, modelling of the material properties and simulations of the process to improve the microreplication quality are still lacking. The principal scientific challenge in the numerical simulation is to provide an efficient material behaviour law to describe the deformation of the material during the process. The physical constitutive behaviour law of polymer plates in the hot-embossing process can be treated as viscoelastic or viscoplastic, depending on the various process boundary conditions. This study mainly concerns the identification of a physical constitutive behaviour law for an amorphous polymer poly (methyl methacrylate) (PMMA), which is used in hot-embossing processes at the microscale. Uniaxial compression tests were carried out under various temperature conditions slightly above the glass transition temperature (Tg) of the polymer, and the viscoplastic behaviour of the polymer was characterised. In the present study, the fabrication of a complex microfluidic device is treated as a case study, focusing on the filling stage of the process. Modelling in numerical software using the implemented polymer behaviour model was realised, and the influence of different processing and material parameters on the filling efficiencywas investigated at the microscale in two different zones (channel and reservoir). Specific related microreplications in the processing temperature range from Tg + 20 °C to Tg + 40 °C with different material parameters were also studied and compared. The results of the simulation were in good agreement with the experimental results in terms of replication for the PMMA amorphous thermoplastic polymer compared at different microscales and in different zones, confirming the efficiency of the proposed approach with different comparisons in 2D and 3D cases. Moreover, the models can be used when similar behaviours are observed in amorphous thermoplastics and extended to other micro hot-embossing components.