Abstract Analytical solutions to the dispersion-convection equation for leaching of saline soils under exponentially decreasing, and arbitrary initial salt profile have been presented. The soil profile is considered semi-infinite and homogeneous. Another solution incorporating an exponentially decreasing time-varying boundary condition at the surface is developed. The effect of the initial condition and solute transport parameters on the predictive behaviour of the model has been studied by arbitrarily choosing of values of the parameters. The results indicate that the prediction accuracy of the model increases if the initial salt distribution profile is represented by a function which approximates this profile closely. The effect of the time-varying boundary condition is negligible for most practical purposes at or below 15 cm depth of the soil profile. The changes in the transport parameter may not only enhance or retard the pace of reclamation but also affect the final salt distribution in the soil profile.