With the aid of Laplace transform, the fundamental solution for the solute transport problems with Dirichlet and Neumann conditions in a semi-infinite saturated, homogeneous soil is derived. Three types of point sources with specific time drop in the soil surface were considered. The analytical solutions for solute concentration distribution with these source inputs are presented. The validity of each solution is analyzed and discussed, individually. The derived solutions are helpful to soil amelioration and other similar computing simulations of solute transport in soil systems.