The derivation of analytical method to examine the stress field near the end of a simply supported, laminated beam is presented. Specific effort has been directed to accurately calculate the transverse shear and normal stress by incorporating the exact displacement relations derived by Kozik (1970). The method accommodates any combination of material lay-rip and any type of normal load on the upper and lower surfaces. The reactions at the ends of the beam may be distributed over the surface edges in a fashion, nest accurately characterizing the physical supports. The solution and application of the method is presented in Part II of this paper.