For highly cross-linked polymer networks bonded to a solid surface, the effect of interfacial bond density and system size on interfacial fracture is studied using molecular dynamics simulations. Results for tensile and shear mode simulations are given. The correspondence between the stress-strain curve and the sequence of molecular deformations is obtained. The failure strain for a fully bonded surface is equal to the strain necessary to make taut the average of the minimal paths through the network from a bonded site on the bottom solid surface to a bonded site on the top surface. At fractional interfacial bond densities, cavities form above the nonbonded surface, yielding an inhomogeneous strain profile and a smaller failure strain. The failure strain and stress are linearly proportional to the number of bonds at the interface except in the tensile mode when number of bonds is so few that van der Waals interactions dominate. The failure mode is successfully constructed to be interfacial by limiting the interfacial bond density to be less than the bulk bond density.