The electronic, linear optic and elastic properties of RbNbO3 crystal have been calculated under pressure using the density functional theory for its five different phases, P-1, Pm-3m, P4mm, Amm2 and R3m. It is shown that RbNbO3 crystal electrically exhibits a semiconductor property under zero pressure in these phases except for triclinic phase, P-1, in which the compound has insulator property. Also, the crystal has a direct band gap in the Amm2 phase while it has an indirect band gap in the other four phases. Moreover, the electronic properties were calculated under pressure and it is shown that the locations of top of the valence band and the bottom of the conduction band in the Brillouin Zone were varied with the effect of pressure. The linear optical functions such as dielectric function, refractive index, absorption and extinction coefficients depend on light frequency were calculated under various pressure values for all phases and it is shown that values of the optical constants change with the effect of pressure. Finally, the elastic stiffness tensor of RbNbO3 were calculated for four phases, Pm-3m, P4mm, Amm2 and R3m and the variations of some elastic constants, such as Debye temperature, Poisson ratio, bulk modulus, shear modulus, and Young modulus, with the pressure were investigated.