The finite maximum length of a steady state contaminant plume is determined by developing and employing a new analytical solution which overcomes two drawbacks associated with existing approaches. First, we account for a sharp front caused by the complete consumption of the pollutant ("electron donor") and some electron acceptor in an instantaneous binary reaction occurring at the front. This approach is not based on purely conservative or first-order degradation models which lead to theoretically infinite plumes and, in addition, depend on a concentration threshold. Second, a vertical aquifer cross section with finite thickness is selected as a model in order to better represent the supply of electron acceptors mostly entering the aquifer from the top. This type of setting allows investigation of the impact of aquifer thickness on plume length. An implicit representation of the donor-acceptor front in a finite vertical domain previously required numerical solutions of the underlying advection-dispersion-reaction equation; we provide for the first time an analytical solution of this two-dimensional transport problem. The length of the plume is found to be given by the point of intersection of the donor-acceptor front and the aquifer bottom. Furthermore, a rather simple and highly accurate approximation is derived to compute the steady state plume length. A comprehensive sensitivity analysis reveals that results are most strongly influenced by aquifer thickness, followed by vertical transverse dispersivity and, to a somewhat lesser extent, by chemical reaction parameters. Longitudinal dispersivity has practically no effect on plume length, and furthermore, there is zero impact of linear velocity. With regard to groundwater risk assessment at the field scale it is also important to note that the present approach is meant to provide an upper bound on the actual plume length. Further research activities may be directed to refine the transport model by considering, for instance, degradation inside the plume and the limited vertical extent of the contaminant source.