The existence of Amide Planes of Protein Structures has been confirmed recently by a Mathematical Programming Approach [1].The proposed cost function is the expression of a dihedral angle in terms of three variables: two bond angles,and the angle corresponding to alpha-carbon geometry.The average value of this dihedral angle is calculated to be 180 degrees by exhaustive statistical analysis of dipeptide structures [2] and this was the first indirect confirmation of Paulings insight on the existence of amide planes of Protein Structure [3].In this work we show how the methods of Mathematical Programing can be applied to derive the same average value which we believe to be the first of a series of introductory results belonging to a new modelling process of biomolecular structure.