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 (partial derivative W/partial derivative I-1) was shown theoretically to be 5 G/8, while the derivatives with respect to I-2 and I-3 (partial derivative W/partial derivative I-2 and partial derivative W/partial derivative 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.