A similarity boundary value problem which describes the steady-state buoyancy induced plane flow next to an impermeable, horizontal surface in porous media saturated with cold water is studied. Numerical solutions are found in two disjoint regions of temperature-ratio parameter R by using a multiple shooting code BVPSOL. In each region, solutions are obtained by applying the continuity process which gives, respectively, a smooth bifurcation curve in term of a appropriate parameter. Multiple solutions are found at some R in this two regions. Some of them are similar and others indicate physically the potential existence of a large amount of energy for any trend arising that drives one steady state to another.