We use an ab initio full-potential linear muffin-tin orbital method within the local density approximation (LDA) to study the structural, elastic, electronic and optical properties of the antiperovskite BiNBa 3 . The calculated lattice parameter is in good agreement with previous calculations. The elastic constants and their pressure dependence are calculated; we found a linear dependence of elastic stiffness on the pressure. We estimated the Debye temperature of this compound from the average sound velocity. We also present results of the effective masses for the electrons in the conduction band (CB) and the holes in the valence band (VB). To complete the fundamental characteristics of this compound we have analyzed the optical properties.