Combined first-principles pairwise simulations and quantum-mechanical ab initio perturbed ion (AIPI) calculations have been extensively performed to determine the static equations of state (EOS) of the cubic (fluorite-type) and orthorhombic (α-PbCl2-type) polymorphs of CaF2. This theoretical investigation covers the range of pressures experimentally available (0–45 GPa). The elastic behavior and the equilibrium crystal parameters have been accurately determined by means of efficient numerical procedures involving a Richardson-iterated, finite-difference formula for the derivatives and the combination of downhill simplex and modified Powell methods for the multidimensional optimizations. For the bulk modulus and the effective elastic constants of the cubic phase, the simulations and AIPI calculations give increasing functions of pressure with small negative curvatures. Besides, the zero-pressure AIPI computations agree with the values of Catlow et al. [J. Phys. C 11, 3197 (1978)] for the bulk modulus and the elastic constants. The computed EOS also reproduces quantitatively the most recent experimental p-V data for the cubic phase. For the orthorhombic phase, we optimize nine crystal parameters for each value of pressure. This set provides a full structural characterization of this phase, as well as a global description of the p-V relationship that is consistent with the synchrotron-radiation x-ray-diffraction study of Gerward et al. [J. Appl. Cryst. 25, 578 (1992)]. Our simulation techniques are able to detect a first-order phase transition from the low-pressure fluorite-type to the high-pressure α-PbCl2-type polymorph. The computed thermodynamic transition pressure lies below the experimental values, as it should for this kind of structural transformation exhibiting large pressure hysteresis.