Abstract: Based on the first linearized Boussinesq equation, the analytical solution of the transient groundwater model for description of phreatic flow in a semi-infinite aquifer bordered by a linear stream with linearly varying stream water levels, was derived through the Laplace transform and in view of the integral property of the Laplace transform. The solution is composed of some common functions and its expression form is relatively simple. According to the mathematical characteristics of the solution, its corresponding physical meaning was discussed. The variation rule of the phreatic level revealed by the solution shows that the temporal variation curve of the aquifer at any point is fixed and has nothing to do with the change rate of the water level of the river channel. The time of the maximum speed change of the phreatic aquifer nonlinearly varies with λ. Based on the variation rule of the phreatic level, the method determining the aquifer parameters with the changing velocity of the phreatic level was established, and the process of obtaining the parameter with the inflection point method was demonstrated through an example.