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Methodology of determining coefficients of material strain energy functions of rubbers from experimental measurements of homogeneous deformations is examined within the scope of the 3rd order deformation theory [3]. Closed-form solutions of most frequently employed material testing deformations - simple tensile, pure shear and equal bi-axial deformations - are examined to reveal the shortcomings of using any one deformation in characterizing the strain energy function, In order to obtain a more representative material strain energy function, employment of more than one homogenous deformation is recommended along with improved material sampling. In situations, however, where data from simple-tensile deformation alone are available a set of constraints on the coefficients have been derived that improves the extrapolation characteristics of the fitted function.