Theoretical investigations concerning the high-pressure polymorphs, the equations of state, and the phase transitions of SnO2 have been performed using density functional theory at the B3LYP level. Total energy calculations and geometry optimizations have been carried out for all phases involved, and the following sequence of structural transitions from the rutile-type (P4(2)/mnm) driven by pressure has been obtained (the transition pressure is in parentheses): -> CaCl2-type, Pnnm (12 GPa) -> alpha-PbO2-type, Pbcn (17 GPa) -> pyrite-type, Pa (3) over bar (17 GPa) -> ZrO2-type orthorhombic phase I, Pbca (18 GPa) -> fluorite-type, Fm (3) over barm (24 GPa) -> cotunnite-type orthorhombic phase II, Pnam (33 GPa). The highest bulk modulus values, calculated by fitting pressure-volume data to the second-order Birch-Murnaghan equation of state, correspond to the cubic pyrite and the fluorite-type phases with values of 293 and 322 GPa, respectively.