The elastic, thermodynamic and optical properties of Li 3 P have been studied for the first time using the plane-wave ultrasoft pseudopotential technique which is based on the firstprinciples density functional theory (DFT) within generalized gradient approximation (GGA). The optimized lattice parameters, independent elastic constants, Young's modulus E, bulk modulus B, shear modulus G, Cauchy's pressure, Pugh's ductility index (G/B), and Poisson's ratio υ have been calculated and discussed. The temperature and pressure dependence of bulk modulus, Debye temperature, specific heats, and thermal expansion coefficient are all obtained through the quasi-harmonic Debye model with phononic effects for T = 0−1000 K and P = 0−35 GPa. The large reflectivity in the ultraviolet energy region between 7-13.4 eV indicates the material to be a good candidate as coating to avoid solar heating.