Existing literature assumes the equality of elastic modulus under both tension and compression loading for all materials. That this is not universally true is demonstrated in the experimental data of some naturally occurring materials presented in the text. In cognisance of this phenomenon, analytical solutions for the elastic deformation of such materials in bending are developed. These are then applied to the experimental results presented in the text to determine the elastic modulus and bending moment of the materials in tension and compression, and to further locate the neutral axis for such dual moduli materials. It is necessary therefore, to take account of the dual moduli phenomenon when using materials that posses this property.