In drylands, poor rains combined with high evaporation rates increase the risks of soil salinization in addition to drought stress. Here, we determined the values of the parameters in the Feddes root water uptake function for sesame (Sesamum indicum L.) under drought and salinity stresses in a pot experiment using “Lebap-55”, which has been bred for the drylands of the Aral Sea Basin but is moderately sensitive to salinity stress. We measured the hourly values of the transpiration, soil moisture, and salinity in the upper and lower soil layers in pots, solar radiation, and root distribution. The values were quantified by two methods. The bulk method uses only daily pot weight data, and the average soil water content and salt concentration are back-calculated from the mass balance. The inverse method uses the monitored values of the soil water content and salinity as well as daily weight data and solar radiation. Both methods could successfully estimate all the parameter values for both stresses. The bulk method performed better under drought stress, even without the measured soil water content or root distribution. It also had satisfactory accuracy in estimating the values under salinity stress. Both methods performed better under drought stress than under salinity stress. The parameter values determined here could be used for irrigation scheduling and salinity management using numerical models for the studied crop.