The structural, elastic, electronic, optical and thermodynamic properties of the sodium polonide Na2 Po compound have been studied through the full potential linearized augmented plane wave plus local orbitals (FP-LAPW + lo) and tight-binding linear muffin-tin orbital (TB-LMTO) methods. The ex-change–correlation potential was treated within the local density approximation for the TB-LMTO calculations and within the generalized gradient approximation for the FP-LAPW + lo calculations. In addition, Tran and Blaha-modified Becke–Johnson (TB-mBJ) potential and Engel–Vosko generalized gradient approximation were used for the electronic and optical prop-erties. Ground state properties such as the equilibrium lattice constant, bulk modulus and its pressure derivative were calculated and compared with available data. The single-crystal and polycrystalline elastic constants of the considered compound were calculated via the total energy versus strain in the framework of the FP-LAPW + lo approach. The calculated electronic structure reveals that Na2 Po is a direct band gap semiconductor. The frequency-de-pendent dielectric function, refractive index, extinction coefficient, reflectivity coefficient and electron energy loss function spectra are calculated for a wide energy range. The variations of the lattice constant, bulk modulus, heat capacity, volume expansion coefficient and Debye temperature with temperature and pressure were calculated successfully using the FP-LAPW + lo method in combination with the quasi-harmonic Debye model. © 2015 The Minerals, Metals & Materials Society.