In this paper, we propose a generalized shock model for the enhancement and restoration of degraded gray-level character images. This model is a quasi-linear hyperbolic partial differential equation with discontinuous coefficients, based on a recently-published work. The model was extended to peeling character shapes with a uniform and centered width of value K. These processing tools may significantly improve the subsequent stages of the character image recognition task. Both models have been tested on a set of gray-level character images of varying quality from the CEDAR database, and experimental results have proved the efficiency and effectiveness of such modeling.