A computer-aided stochastic model of the radiolysis of liquid water has been developed. It is based on Monte Carlo simulation of charged-particle tracks, a random-flight method to simulate diffusion of species and the Debye-Smoluchowski theory of reactions between radicals. The model takes into account the formation of ionizations, excitations and subexcitation electrons at the physical stage. The corresponding initial yields at approximately 1 fs were found to be G(ion) = 4.37, G(exc) = 2.81 and G(e-sub) = 4.38. The energy spectrum of subexcitation electrons has been calculated. Autoionizations and dissociations of excited molecules, hole migration, electron thermalization, geminate recombination and the cage effect are considered at the physico-chemical stage. The mean thermalization distance of subexcitation electrons is 24.5 nm. The initial yields of e(aq)-, H+, OH, H, H2 and O are 4.89, 4.86, 5.96, 1.10, 0.15 and 0.15, respectively. The reactions between radicals and products as well as their diffusion are simulated at the chemical stage. The decay kinetics of the most important radicals is reported together with the time evolution of the most important reactions. The yields of the reactive radicals, e(aq)-, H+, OH, H and OH-, at 1 ps are 4.84, 4.85, 5.87, 1.09 and 0.0, respectively. The respective steady-state yields at 10 micros are 2.70, 3.58, 2.89, 1.17 and 0.79. The yields of molecular products, H2O2 and H2, are 0.73 and 0.47 at 10 micros. The concentration-dependent yields of e(aq)-, OH and H2O2 are calculated in three different aqueous solutions. The predictions of the model agree fairly well with experimental data.