The well-known phenomenon of the blocking of crystal growth at low supersaturations by a low density of immobile impurities adsorbed on the crystal surface has been investigated by the Monte Carlo technique. The computer simulations were carried out for [100] steps on the (OO1) face of a solid-on-solid Kossel crystal covered by a square array of immobile impurities. Above and slightly below the roughening temperature, blocking of crystal growth was found to be due to the creation of an extra internal surface free energy as a result of the incorporation of impurities. Here the width of the dead supersaturation zone is inversely proportional to the squared distance between the impurities. At lower temperatures growth is blocked by pinning of the growth steps at the impurity centres as proposed in an early paper by Cabrera and Vermilyea (1958), in which the width of the ''dead zone'' is inversely proportional to the impurity separation. Further issues addressed to in this paper are a kinetic impurity blocking for rough faces and the blocking of step propagation by randomly deposited impurities as well as by the smallest possible impurities of one growth unit in size.