The dissolution of nonaqueous phase liquids (NAPLs) trapped at residual saturation is an important problem at many contaminated groundwater sites. It is well known that NAPL ganglia trapped within the pore space reduce the permeability of the medium to aqueous phase flow. When fluid flow is imposed on such a system, the aqueous phase may interact with the dissolution-induced permeability changes, leading to fingered patterns. This mechanism is very similar to that of mineral dissolution instabilities, which are a particular example of reactive infiltration instabilities. Extending that literature, we present a nonlinear model describing the dissolution of NAPL ganglia and perform a linear stability analysis of the resultant moving free boundary problem, demonstrating that instabilities may develop from a planar dissolution front. Predicted finger wavelengths are a function of both residual NAPL saturation and the imposed aqueous phase flow rate; they range from centimeters to meters. Experimental observations of dissolution fingering are presented in a companion paper <Imhoff et al., this issue> and are compared with predictions from this model. Dissolution fingering may affect the solubilization of NAPL ganglia in natural environments and in experimental studies of NAPL dissolution intended to quantify mass transfer rates. ¿ American Geophysical Union 1996