This paper addresses the damage and fracture issues of glass and ceramic materials used in solid oxide fuel cells. Analyses of an internal crack and of an interface crack between dissimilar materials were conducted using a modified boundary layer modeling approach. In this approach, fracture is allowed to occur in a small process window situated at an initial crack tip. Elastic displacement crack-tip fields are prescribed as remote boundary conditions. Crack propagation was first modeled discretely. Next, a continuum damage mechanics (CDM) model for brittle materials was developed to capture damage and crack growth in the process window. In particular, the damage model was applied to a glass-ceramic material that had been developed in-house for sealing purposes. Discrete and continuum damage solutions were then compared. Finally, the CDM model was used to determine the crack propagation direction as a function of a mode mixity measure.