The experimental and theoretical investigation of the mechanical properties of an ethylene-propylene-diene terpolymer (EPDM) elastomer reinforced with carbon black was examined. The material constants of the testing material were determined by plotting the stress-strain experimental curve in a reduced stress versus the inverse stretch diagram. The Ogden equation was used for the strain energy function to fit uniaxial experimental stress-strain curves. The characterization of the material was examined using the contour maps of partial derivativeW/partial derivativeI(1) and W partial derivativeW/partial derivativeI(2), i.e., of the derivatives of strain energy function with respect to strain invariants I-1 and I-2.