A dense inflow from a river into a lake or reservoir initiates gravity currents through a plunging process with intense mixing. The classic two-controlvolume theory for the analysis of plunging phenomena has been recently corrected. In particular, the design of one of the two control volumes does not follow physical principles and has undesirable implications. Herein, a generalized theoretical framework is developed for the analysis of plunging flows. Two general cases are considered to clarify the effects of the bottom slope and the inflow densimetric Froude number on the plunge condition. It is demonstrated that the relations between the dimensionless parameters characterizing the plunging phenomena in these two cases are generically different. The present theory is compared with the two-control-volume theory, the latter of which only partially explains the influence of the inflow densimetric Froude number. Good agreement between the present theory and reported data is found.