While flowing through porous medium, ground water flow dissolves minerals thereby in creasing medium porosity and ultimately permeability. Reactive fluid flows preferentially into highly permeable zones, which are therefore dissolved most rapidly, producing a further preferential permeability enhancement. Accordingly, slight non-uniformities present in porous medium can be amplified and lead to fingering reaction fronts. The objective of this study is to investigate dissolution-induced porosity changes on reaction front morphology in homogeneous porous medium with two non-uniformities. Four controlling parameters, including up stream pressure gradient, reaction rate constant, non-uniformities spacing and non-uniformity strength ratio are comprehensively considered. By using a modified version of the numerical code, NSPCRT, to conduct a series of numerical simulations, front behavior diagrams are constructed to illustrate the morphologies of reaction fronts under various combinations of these four factors. Simulation results indicate that the two non-uniformities are inhibited into a planar front under low up stream pressure gradient, merge into a single-fingering front under inter mediate up stream pressure gradient, or grow into a double-fingers front under high up stream pressure gradient. More over, the two non-uniformities tend to develop intoadouble-fingering front as the non-uniformity strength ratio in creases from 0.2 to 1.0, and merge into a single-fingering front while the non-uniformity strength ratio in creases from 1.0 to 1.8. When the reaction rate constant is small, the two non-uniformities merge into a single front. Reaction rate constant significantly affects front advancing velocity. The front advancing velocity decreases with the reaction rate constant. Based on these results, front behavior diagrams which de fine the morphologies of the reaction fronts for these four parameters are constructed. Moreover, non-uniformity strength ratio and reaction rate constant are identified as two important factors that govern the interaction of dissolution and solute transport in groundwater systems.