Simulating semi-solid metal forming requires modelling semi-solid behaviour. However, such modelling is difficult because semi-solid behavior is thixotropic and depends on the liquid-solid spatial distribution within the material. In order to better understand and model relationships between microstructure and behavior, a model based on micromechanical approaches and homogenisation techniques is presented. This model is an extension of a previous model established in a pure viscoplastic framework to account for elasticity. Indeed, experimental load-displacement signals reveal the presence of an elastic-type response in the earlier stages of deformation when semi-solids are loaded under rapid compression. This elastic feature of the behaviour is attributed to the response of the porous solid skeleton saturated by incompressible liquid. A good quantitative agreement is found between the elastic-viscoplastic predicted response and the experimental data. More precisely, the strong initial rising part of the load-displacement curve, the peak load and the subsequent fall in load are well captured. The effect of solid fraction on mechanical response is in qualitative agreement with experiments.