Recent experiments by Wang (1990) on copper bicrystals with a [110] symmetric tilt of 38.9 degrees have shown that the mode of fracture of these bicrystals, i.e., whether fracture is of a ductile or brittle nature, depends on the direction of cracking. An analysis of this effect within the framework of continuum crystal plasticity is presented. The formulation accounts for finite deformations and finite lattice rotations, as well as for the full three-dimensional collection of slip systems in FCC crystals. Our results indicate that, whereas the level of stress ahead of the crack tip is similar for the ductile and brittle cracking directions, the sizes of the plastic regions differ significantly in the two cases.