Motivated by mechanical metamaterials with unique elastic properties this project focusses on linear elasticity with multiscale high-contrast coefficients. In this setting, a critical coupling between the fine length scale and the contrast is crucial. The goal is to design and analyze the Heterogeneous Multiscale Method (HMM) for periodic setups, combining finite and virtual elements for effective meshing. Additionally, it explores the formulation of HMM in high-contrast settings and the effects of varying geometries on multiscale basis functions beyond the periodic set-up.