Structural, elastic, electronic and thermodynamic properties of ZrSi₂ have been investigated by means of first-principles plane wave pseudopotential calculations combined with the quasi-harmonic Debye model. We find that the orthorhombic base-centered lattice structure (C49) ZrSi₂ is mechanically stable up to 80 GPa according to the elastic stability criteria, and there is a transition from brittle to ductile nature at about 56.5 GPa. The calculated elastic anisotropy factors suggest that ZrSi₂ is anisotropic and the degree increases with pressure. In addition, the bonding characteristics are discussed by analyzing the energy band structure, charge density distribution and Mulliken populations. The pressure and temperature dependences of the bulk modulus, specific heat, Debye temperature and thermal expansion coefficient are also discussed through the quasiharmonic Debye model.