Abstract: In this Paper, the bead-spring model of N identical beads advanced by Rouse is extended to that of a polymer solution with molecular weight distribution, and the rheological equation of state for the modified Rouse model with different chain lengths is obtained. According to some usual molecular weight distributions, the material functions, such as non-newtonian viscosity and first normal stress coefficient, for the steady-state shear flow and, therefore, the relationship between the intrinsic viscosity and the weight average degree of polymerization are derived. The results show that the linear viscoelastic behavior of this model depends on molecular weight distribution greatly. The kinetic pracess of polymerization can be predicted by measuring the rheological parameters of the system.