Results of model calculations for class II methanol masers (MMII) are presented. The model of the pumping assumes that an external dust layer provides the source of energy for maser excitation. The dependence of the emergent maser spectrum on the properties of the dust layer is studied. These properties include the chemical composition and sizes of dust grains, the temperature and optical depth of the dust layer. as well as the dilution factor of external dust emission. It is shown that, in order to reproduce the observed patterns of class II methanol maser line ratios, the pumping dust layer should be mostly composed of silicate grains with sizes smaller than 0.01 μ. It is shown that the layer of warm (> 125 K) dust effectively pumps the strongest MMII transitions over a wide range of 30 μ dust opacities (0.01–2) and dilution factors (0.02–0.5).