Due to the fact that most of closed-end canals are protected from high energy inputs, these canals tend to act as sediment traps. Accumulation of deposited material creates navigational and flood problems. Shoaling in closed-end canals is caused mostly by fine sediments. The behavior of fine sediments can be quantitatively described by means of a mass balance equation. More specifically, the advection-dispersion equation including proper sink/source terms can be used. The sink/source terms represent the processes of deposition and erosion respectively. The purpose of this thesis is to develop analytical solutions of the unsteady advection-dispersion equation as applied to free surface closed-end canals. Solutions are obtained under various initial and boundary conditions, by using the finite transformation analysis. The simulation results are validated against laboratory data.