Globular proteins fold into compact particles with interior amino acid residues shielded from the surrounding aqueous environment. An early hypothesis holds that entropic hydrophobic forces drive this phenomenon. However, previous analyses based on a binary description of the accessible surfaces of amino acid residues in proteins did not support this hypothesis. This report shows that a complete description of accessible surface areas is given by parametric distribution functions with three modes. The modes are formed by partitioning the available accessible surface area of the amino acids into three segments; the data for each segment are characterized by a mode-specific model. In the "repulsive" mode, probabilities of accessibility decrease exponentially with exposed surface area, as predicted by the hydrophobic hypothesis. A distinct "buried" mode is needed to account for an excess of residues at or near zero accessibility for most amino acids, consistent with the use of binary descriptions of accessibility. A third mode exists which is termed "near neutral" because it is described by a nearly uniform distribution of accessibility for the hydrophilic amino acids. Empirical energies calculated for the repulsive mode correlate well with measured free energies of transfer of amino acids from water to organic solvents, while those from the buried mode correlate well with measured free energies of hydration of the side chains. Poor cross correlations between these energies give an explanation for the previous conflict in interpreting these data.