Geochemical and field evidence suggest that melt transport in some regions of the mantle is localized into mesoscale channels that have widths of 0.1--100 m or larger. Nevertheless, the mechanisms for formation of such channels from a grain-scale distribution of melt are poorly understood. The purpose of this paper is to investigate one possible mechanism for channel formation: the reaction infiltration instability (RII). We present numerical solutions of the full equations for reactive fluid flow in a viscously deformable, permeable medium. We show that dissolution in a compactible solid with a vertical solubility gradient can lead to significant flow localization such that >90% of the melt flux is channelized in <20% of the available area. In particular, the ability of the solid to compact enhances the instability by forming impermeable regions between channels. The combination of reaction, diffusion, and solid compaction leads to strong selection of preferred length scales with channel spacing smaller than the compaction length (Δ~102-104 m). We explore the evolution of dissolution channels over parameter space and show that the behavior of the full nonlinear solutions is consistent with predictions from linear stability analysis. We also briefly consider the behavior of the instability in the presence of melting due to adiabatic decompression and demonstrate that significant localization can occur even in the presence of uniform melting and compaction. Using the linear analysis to extend these results for parameters expected in the Earth's mantle suggests that robust channel systems could form through the RII from a homogeneous system in ~100,000 years with dominant channel spacing of 1--200 m. ¿ 2001 American Geophysical Union