The resolution of photolithographic processes has advanced to the point that difficulties, such as line-edge roughness, associated with phenomena occurring at molecular length scales are becoming important. In order to control these phenomena, it is necessary to understand them. To that end, a numerical model has been used to simulate the dissolution of phenolic polymers in aqueous base. The simulation applies the Critical Ionization Model to a rectangular-lattice representation of the polymer matrix. The model has been adapted to describe the dissolution process that is responsible for photoresist function. Both continuum and molecular versions of the model are presented. The Continuum Model yields dissolution profiles that approximate the contours of the calculated spatial variations in chemical blocking (blocking profile). An algorithm has been developed to connect individual cells to form polymer chains, and to fill the lattice in a way that produces a Gaussian chain length distribution. The model employs only a single adjustable parameter, the time-step correction factor (assuming one can measure the probability of ionization once a site encounters the developer). The Molecular Model predicts a dissolution rate that decreases non-linearly with respect to degree of chemical blocking, as is observed experimentally. Dissolution profiles can be generated with the Molecular Model based either on this calculated dependence of the dissolution rate on blocking fraction or from direct application of the model to a blocking profile. The probabilistic nature of the model introduces edge roughness of the same degree as that observed experimentally.