Elastic properties of segmented polyurethaneureas (SPUs) under pure shear deformation were investigated. Data were analyzed by using strain energy density function (W). The values of the derivatives of W with respect to the invariants of the strain tensor (I i ; i = 1, 2, 3 ) at zero strain limit were also estimated theoretically and were compared with those estimated by experiment. The limiting value of the derivative with respect to I 1 (∂W/∂I 1) was shown theoretically to be 5 G/8, while the derivatives with respect to I 2 and I 3 (∂W/∂I 2 and ∂W/∂I 3 were respectively-G/8 and -3G/8. The theoretical prediction could explain the asymptotic behavior of the derivatives of SPUs as well as isoprene rubber (IR) reported by Kawabata et al. at small I 1 limit.