Ab initio quantum mechanical methods have been used to examine clusters formed of molecules of methane and water. The clusters contained one molecule of one component (methane or water) and several (10, 8, 6, 4, and 1) molecules of the other component. The Mphiller-Plesset perturbation theory (MP2 method) was used in the calculations. The cluster geometries were obtained via optimization and the interaction energies between the nearest neighbors were calculated for the geometries obtained in the first step. It is shown that the interaction energies and intermolecular distances between the molecules of methane and water are quite different in the clusters CH4...(H2O)(10) and H2O...(CH4)(10). They are also different from those in the water/ methane dimer. The structure of the cluster CH4...(H2O)(10) is highly affected by the hydrogen bonding among the water molecules, and the methane molecule is located inside a cage formed of water molecules. In contrast, the molecules of methane and water are randomly distributed in the cluster H2O...(CH4)(10). The average methane/ water intermolecular distance in the cluster CH4...(H2O)(10) provided by the quantum mechanical calculations is in agreement with the experimental and simulation results regarding the position of the first maximum in the radial distribution function g(oc) = g(oc)(r(oc)) in dilute mixtures of methane in water, where roc is the distance between the C atom of methane and the O atom of water. It is shown that the water molecules in the vicinity of a central methane molecule can be subdivided into two groups, A and B. Molecules of type A are touching nearest neighbors of the central methane molecule. They are located on a sphere with a radius corresponding to the first maximum in the radial distribution function goc = goc(r(oc)) and are tangentially oriented toward the central methane molecule. The layer of A water molecules is somewhat denser than bulk water. The molecules of type B are also located in the first hydration layer of a central methane molecule (up to a distance given by the position of the first minimum of the radial distribution function g(oc) = g(oc)(r(oc))), but are not touching nearest neighbors. They are distributed more randomly than the molecules of type A, because they are less affected by the hydrophobic core of the solute.