A Monte Carlo Glauber model of multiple production at high energies has been developed. A generalization has been made to the case of proton-nucleus and nucleus-nucleus collisions. It is shown that in pp collisions the total, elastic and inelastic cross sections and the slope of the difraction cone are satisfactorily described in a wide energy range. The model is applied to Pb-Pb collisions at LHC energies. A relation to modified Glauber model and other approaches is discussed.