The governing equations for miscible contaminant transport in saturated porous media with release effect are developed under the 1-D seepage condition, and an elementary solution is derived using the Laplace and Fourier transforms and their inverse transformation for the case of a point contaminant source which is instantaneously released from the surface of a half-space body. Then the analytical expression of the contaminant concentration in porous medium subjected to a circular contaminant source is derived from the elementary solution. A calculation example for cyclic contaminant source is analyzed. It is shown that the contaminant concentration in a porous medium varies in a cyclic manner under a cyclic contaminant source applied on the porous surface, and finally reaches a quasi-steady state with the same cyclic period as the contaminant source. However, the phase of concentration fluctuation at a given depth lags behind the contaminant source. At steady state, the cyclic period of contaminant concentration in the porous medium is the same as that of the contaminant source. In practice, as the contaminant source cyclically fluctuates at the surface of porous medium, the concentration of contaminant in a porous medium around the surface also increases or decreases alternately in the direction. On the other hand, the contaminant gradually penetrates towards depth and eventually reaches a definite depth away from the surface.