An attempt has been made to establish a general theory of the random packing of particles. The existence of two packing mechanisms, viz., the filling mechanism and the occupation mechanism, is demonstrated and the result used to explain the limitations of the existing geometric/linear mathematical models. An analytical model, based on the experimental results of binary mixtures and the experimental theory of mixtures is developed to estimate the porosity of multicomponent mixtures. Comparison of model predictions with the measurements of ternary mixtures, Gaussian and log-normal size distributions shows its high order of predictability. The application of the model to irregular particle systems is also discussed.