Systematic investigation of the ground state structure, which includes elastic and transport properties, of perovskite oxides REMnO₃ (RE = Ce and Pr) has been carried out by first principles calculations. We present the analytical as well as DFT calculated equilibrium lattice constants which show good agreement with experimental data. Three independent elastic constants are emphasised to yield the corresponding mechanical properties, including the elastic moduli (B, G and Y), Poisson's ratio (ν), anisotropy factor (A) and Pugh ratio B/G, for these compounds. These calculations predict the brittle PrMnO₃ as a less hard material than the ductile CeMnO₃ oxide. Post DFT treatment involving Boltzmann's theory is conveniently employed to investigate the thermoelectric properties of these compounds. The analysis of the thermal transport properties specifies the dimensionless figure of merit of 0.24 and 0.19 at room temperature for PrMnO₃ and CeMnO₃, respectively. Their half-metallic nature with efficient thermoelectric parameters, including electrical conductivity, Seebeck coefficient and thermal conductivity, suggest the likelihood of these materials to have a potential application in the design of shape memory devices and imminent thermoelectric materials.