The relative phase stability of the C- and A-type polymorphs of rare-earth sesquioxides $R{E}_{2}{\text{O}}_{3}$ ($RE=\text{La}$, Ce, Pr, Nd, Pm, Sm, Gd, Er, and Lu) under pressure have been studied by ab initio methods based on density-functional theory within the local-density approximation (LDA), and generalized gradient approximation. Both functionals show that the pressure of the C- to A-phase transition increases in the oxide series, although, the LDA results appear to be in better agreement with experimental data. The equation of states and pressure dependence of bulk modulus, $c/a$ ratio and other structural parameters are analyzed. Our results indicate that the phase stability in these oxides to a large extend is determined by the electrostatic contribution to the total energy and it is related to the relaxation pattern of the structures.