The phase transformation of CeO2 and ThO2 from fluorite to cotunnite-type structure under pressure is predicted within the density functional theory implemented with the GGA-PW91 method, the pressure induced structural phase transition occurs at 28.9 GPa for CeO2 and 29.8 GPa for ThO2. These values are in excellent agreement with the experimentally measured data. The elastic, electronic and optical properties at normal as well as for high-pressure phase have been calculated, particular attention is devoted to the cotunnite phase. Further, the dependence of the elastic constants, the bulk modulus B, the energy band gaps and the dielectric function on the applied pressure are presented.Highlights► Phase transition of CeO2 from fluorite to cotunnite-type structure at 28.9 GPa. ► Phase transition of ThO2 from fluorite to cotunnite-type structure at 29.8 GPa. ► The elastic constants and bulk modulus of CeO2 increase under pressure. ► The band gaps of CeO2 and ThO2 increase under pressure. ► The dielectric functions of CeO2 and ThO2 in cotunnite structure are calculated.