In the seepage region without the free surface, the seepage face is formed at the pervious boundary which faces to the atmosphere. At this pervious boundary, two following phenomena generally occur. One, the seepage face is formed at the whole pervious boundary, and the other, the seepage face is only formed at lower part of the pervious boundary and the rest of the boundary plays the role of an impervious boundary. Which phenomenon taking place at this boundary would depend upon the condition imposed on the seepage region. For example, in Fig.1, corresponding to the seepage flow into a ditch in the confined aquifer, the seepage face is formed at one portion of the pervious boundary facing to the atmosphere. In this case, the phenomenon in which the whole pervious boundary becomes the seepage face can not take place under the condition that Darcy's law is valid. In Fig.7, corresponding to the flow into an infiltration gallery in the stratified stratum, there are two following cases in accordance with the stratum conditions and boundary conditions. One is the seepage face formed at the whole gallery wall and the other is the one formed partly. The author has proposed the method of analyzing the problems of the steady saturated seepage flow with the seepage face but without the free surface under the following assumptions. (1)Water starts or stops seeping out of the porous medium towards the atmosphere when the water pressure increases or decreases and finally equal to the atmospheric pressure. (2)Water and air do not flow into the porous medium from the atmosphere. Using this method, the above mentioned seepage flows were analyzed and sufficient results explaining these phenomena were obtained. Whether the air flows into the porous medium or not through the pervious boundary can be judged from this results.