A study was made of a series of one-layer and two-layer models of graphite surface and especially of interactions in the two-layer models. Seven one-layer models, of increasing size up to seven rings, in the C6n2H6n series were calculated for reference purposes with the Hartree-Fock method. Four two-layer models with different stacking sequences (AA, ABAB, and ABCABC) were studied with second-order Moller-Plesset perturbation method using basis set 6-31G*, and one model (ABAB) was also studied with 6-311G* and 6-311G** basis sets. Properties such as charge distribution and density of energy states were compared for the different models. Optimal interlayer distance for (C24H12)(2) with MP2 method and 6-31G* basis was 3.41 Angstrom and for the three C24H12-C6H6 models of different stacking sequence about 3.5 Angstrom, which agrees fairly well with the experimental value of 3.35 Angstrom. The BSSE corrected MP2 interaction energy for (C24H12)(2) was -78.1 kJ/mol, whereas interaction energies for the three C24H12-C6H6 models were in the range of -21.8 to -22.8 kJ/mol. The bigger basis set 6-311G** gave almost twice as strong an interaction for ABAB, -38.8 kJ/mol, as did the 6-31G* basis set. Optimal interlayer distances for ABAB model were 3.29 Angstrom with 6-311G* and 6-311G* basis sets.