Plant cell expansion depends on turgor pressure which provides the energy for cell expansion. Osmoregulatory mechanisms such as the activity of vacuole invertases (VIN) lower the water potential of the cell which leads to water influx and an increase in turgor pressure. The permeability of plasmodesmata is also an important factor to the regulation of fluxes of water and solutes. Plasmodesmata are lined membrane channels that allow free movement of molecules that are smaller than the size exclusion limit of the channel and whose permeability changes during plant development. Experimental studies have correlated changes in the permeability of plasmodesmal channels to turgor pressure variations. Here we study the role of plasmodesmal permeability relative to other factors such as VIN activity and the permeability of the plasma membrane. To address these questions, we use Lockhart’s model for irreversible cell expansion of the cotton fiber with the addition of plasmodesmal-dependent movement of water and solutes. We performed a sensitivity analysis to changes in values of parameters and find that plasmodesmal permeability is among the most important factors for the overall behavior of the system and particularly to building up turgor pressure and expanding cotton fibers. Moreover, we find that non-monotonic behaviors of turgor pressure that have been reported previously in cotton fibers, can not be recovered when the dynamic changes of plasmodesmal permeability are removed. Our results support a model in which the changes in plasmodesmal permeability are important for the regulation of turgor pressure and the expansion of cotton fibers.