Free energy simulation methods are used to analyse the effects of the mutation Arg-96----His on the stability of bacteriophage T4 lysozyme and of Ile-96----Ala on the stability of barnase. By use of thermodynamic integration, the contributions of specific interactions to the free energy change are evaluated. It is shown that a number of contributions that stabilize the wild-type or the mutant partially cancel in the overall free energy difference; some of these involve the unfolded state. Comparison of the results with conclusions based on structural and thermodynamic data leads to new insights into the origin of the stability difference between wild-type and mutant proteins. For the charged-to-charged amino acid mutation in T4 lysozyme, the importance of the contributions of more distant residues, solvent water and the covalent linkage involving the mutated amino acid are of particular interest. Also, the analysis of the Arg-96 to His mutation with respect to the interactions with the C-terminal end of a helix (residues 82-90) indicates that the nearby carbonyl groups (Tyr-88 and Asp-89) make the dominant contribution, that the amide groups do not contribute significantly and that the helix dipole model is inappropriate for this case. For the non-polar-to-non-polar amino acid mutation in barnase, the solvent contribution is unimportant, and covalent terms are shown to be significant because they do not cancel between the folded and unfolded state.