We investigate the probability X that a random mutation (i.e. the substitution in a random site of one amino acid residue by randomly chosen residue) will be a neutral one, i.e. it will not lead to a change in structure. Using a random energy model for the description of protein energy "levels" we show that this probability depends only on stiffness of a chain which is characterized by the number of conformations per peptide bond gamma. The result is X approximately gamma -8. The application of this result for protein engineering experiments and for possible scenario of neutral evolution is discussed.