In this paper, we study the structural, electronic, elastic and thermodynamic properties of the cubic (pm-3 m) NaTaO3 and KTaO3 by Density Functional Theory method (DFT) using the full potential linearized augmented plane wave with local orbital (FP-LAPW)+lo. In this approach the Generalized Gradient Approximation (GGA-PBE96, GGA-PBEsol “Perdew et al. 2008”, GGA-WC06 “Tran et al. 2007”) is used for the exchange–correlation potential. Also we have used the Engel–Vosko GGA and the modified Becke–Johnson potential (mBJ) formalisms which attained considerable success in describing the band structure calculations of many materials. Bulk properties such as equilibrium lattice constants, bulk modulus and its pressure derivative in both compounds are determined and compared to available experimental and theoretical data. Our calculations show that GGA-PBEsol provides an enhancement in lattice parameter prediction of ∼0.03% and ∼1% respectively compared to GGA-WC06 and GGA-PBE96. The elastic constants and their related parameters (Young’s modulus, shear modulus and Poisson ratio) are calculated for these compounds and compared with available previous results. Finally, we have analyzed the thermodynamic properties using the quasi-harmonic Debye model.