Starting pressure gradient introduces a new concept-moving boundary-into the flow in porous media. In order to clarify the property of moving boundary, a theoretical study is conducted on the pressure propagation in reservoirwith starting pressure gradient. According to the study, a reservoir can be divided into two zones: flowing zone and non-flowing zone, while starting pressure gradient exists. The division between the two zones is called moving boundary. Howeverfromthe moving boundary, a paradox comes out that the fluid in non- flowing zone can flowand can not flowsimultaneously. Flow theory in porous media can not be self-consistent. Moving boundary comes fromstaring pressure gradient. But staring pressure gradient is not existing and just a misleading experimental phenomena. So moving boundary does not truly exist. Removal of moving boundary makes the theory of flow in porous media selfconsistent perfectly.