The derivatives of the strain energy function u with respect to the invariants of the strain tensor (I-1 and I-2) are estimated for uncross-linked butadiene rubber by using the BKZ constitutive equation. The derivatives at small deformations show anomalous behavior; namely, an upturn for. partial derivative u/partial derivative I-1 and a downturn for partial derivative u/partial derivative I-1 take place, as is the case of cross-linked rubbers. At large deformations, u is well described by u = A(1)(I-1-3) + A(2)(I-2-3) with numerical constants A(1) and A(2). This behavior is also quite similar to that for cross-linked rubbers. The non-zero positive constant A(2) for the melt suggests that the non-zero value is due to neither the inhomogeneity in network structure nor high extension of constituent polymer chains.