An unsolved issue in simulating the hot embossing of polymers is modelling the unfilled structured mould. This is because the constitutive law of such polymers has not been adequately determined, especially at the microscale or smaller. The present study investigated the influence of the elastic-viscoplastic behaviour on the filling efficiency of an amorphous polymer during the micro hot embossing process. Constitutive equations based on the two-layer viscoplastic model were used to simulate the hot embossing process. The micro-cavity of the mould was completely filled by the polymer, and the elastic, viscous, and plastic behaviours were considered simultaneously in the simulation. Compression tests were performed to identify the model parameter values for poly-methyl methacrylate. A numerical simulation was performed to analyse the contributions of the polymer’s elastic, viscous, and plastic behaviours. The unfilled area in the micro-cavity was evaluated after a displacement of 0.2 mm was applied to the mould. This was used as an indicator to compare the mould filling efficiency with those of the elastoplastic and elastic-viscoplastic constitutive models. The analysis led to the selection of an optimal elastic-viscoplastic model to completely fill the micro-cavity, which was consistent with the experimental results.