Using density functional total energy calculations the structural phase stability and pressure-induced structural transition in different polymorphs of ZnSiO₃ and Zn₂SiO₄ have been studied. Among the considered monoclinic phase with space groups (P 2₁/c) and (C 2/c), rhombohedral and orthorhombic (Pbca) modifications the monoclinic phase (P 2₁/c) of ZnSiO₃ is found to be the most stable one. At high pressure monoclinic ZnSiO₃ (C 2/c) can co-exist with orthorhombic (Pbca) modification. Differences in equilibrium volume and total energy of these two polymorphs are very small, which indicates that it is relatively easier to transform between these two phases by temperature, pressure or chemical composition. It can also explain the experimentally established result of metastability of the orthorhombic phase under all conditions. The following sequence of pressure-induced structural phase transitions is found for ZnSiO₃ polymorphs: monoclinic monoclinic rhombohedral . Among the rhombohedral (), tetragonal , orthorhombic (Pbca), orthorhombic (Imma), cubic and orthorhombic (Pbnm) modifications of Zn₂SiO₄, the rhombohedral phase is found to be the ground state. For this chemical composition of zinc silicate the following sequence of structural phase transitions is found: rhombohedral tetragonal orthorhombic orthorhombic (Imma) cubic orthorhombic (Pbnm). Based on the analogy of crystal structures of magnesium and zinc silicates and using the lattice and positional parameters of Mg₂SiO₄ as input, structural properties of spinel Zn₂SiO₄ have also been studied.