Steady shear rheological measurements are carried out on lyotropic aqueous solutions of hydroxypropylcellulose. The molecular weight is the main parameter investigated. Careful sealing of the sample permits very long time experiments, thus leading to steady‐state measurements at shear rates as low as 10−3s−1. At such low deformation rates, for two of the three molecular weights investigated, a Newtonian plateau is found before region I in the viscosity curve, thus ruling out the possibility of a yield stress in this material. A phenomenological model is proposed in order to interpret the effects of molecular weight on the rheological behavior. The polymer system is modeled as a structured fluid, in which the low shear rate response is dominated by the polydomain structure, whereas molecular dynamics dominates the high velocity gradient region. The model is able to predict the observed qualitative changes in the viscosity vs shear rate curve as a function of molecular weight, as well as the scaling of the first normal stress difference with a molecular time scale of the system. Finally, intrinsic viscosity measurements show that the molecular weight of the samples used in this work is systematically larger than the value indicated by the supplier.