A new method is described for determining the primary elastic constants (stiffnessescij’s and compliancessij’s) with respect to the crystallographic axes. Although we will consider only cubic materials the method can be applied to materials of lower symmetry. The method utilizes the symmetry present in a textured (preferred growth) foil and can be used for cases when bulk single crystals are difficult to prepare for ultrasonic experiments. The method involves the use of expressions, that have not been previously derived, relating the biaxial, flexural, Young’s and shear modulus to the primary elastic constants for textured foils. The agreement of the experimentally observed moduli with ones calculated from the expressions to be presented demonstrates that the accuracy is comparable with existing methods.