The propagation of neutrons in thick paraffin and lead layers was examined in the energy range 0.001 eV-20 MeV. The total frequencies of the neutron occurrence, the frequency distributions of certain lateral displacements of neutrons, the frequency distributions of the neutron occurrence in certain energy regions and occurrence frequencies in certain time intervals were calculated by Monte-Carlo methods as functions of the depths in the materials. Experimental values were used for the total and differential cross sections of different kinds of neutron-nucleus collisions, but for differential cross sections, theoretical estimates were also needed in certain regions. The initial energies of neutrons were 1, 10, and 20 MeV. The effect of the exceeding of the threshold of inelastic reactions in n-C and n-Pb collisions on the frequencies of neutron occurrence was also investigated. The results demonstrate that the frequency of neutron occurrence in lead in different depths is at least one order of magnitude greater than in paraffin. Thus, by combining these two materials in different ways the shape of the occurrence frequency and its absolute height can be modified considerably.