Uniaxial extensional stress growth of a lyotropic liquid crystalline polymer solution consisting of 40 wt % (hydroxypropyl)cellulose in glacial acetic acid was measured using a filament stretching technique. The Doi molecular theory and a modified Leslie-Ericksen continuum theory were used to predict the experimental results. While the Doi theory agreed with both steady shear and steady extensional data, it failed to predict the transient stress growth data. On the other hand, the modified Leslie-Ericksen theory gave a better qualitative prediction of the transient curve, although it predicted that both steady shear viscosity and steady extensional viscosity were constants. The steady state data agrees with the results obtained by Metzner et al., who used a fiber-spinning technique.