In recent years, the scientific community has shown an increasing interest in regards to the investigation of novel materials for the intercalation of lithium atoms, suitable for application as cathodes in the new generations of Li-ion batteries. Within this framework, we have computed the relative structural stability, the electronic structure, the elastic and dynamic properties of Li2MSiO4 compounds (M = Mn, Co, Ni) by means of first-principles calculations based on density functional theory. The so-obtained structural parameters of the examined phases are in agreement with previous reports. The energy differences between different polymorphs are found to be small, and most of these structures are dynamically stable. The band structures and density of states are computed to analyse the electronic properties and characterise the chemical bonding. The single crystal elastic constants are calculated for all the examined modifications, proving their mechanical stability. These Li2MSiO4 materials are found to present a ductile behaviour upon deformation. The diffusion coefficients of Li ions, calculated at room temperature for all the examined modifications, reveal a poor conductivity for this class of materials.