We present a three-dimensional model for the formation of crenulations in ductile shear zones, based on compatibility conditions, infinitesimal-displacement equations, and our own field observations. In many shear zones, at least two and probably three mesoscopic slip systems are active. Crenulation slip is interpreted to compensate for the displacement component of foliation slip normal to the shear zone wall. In zones in which foliation slip is an important mode of deformation, foliation and crenulation slip vectors do not necessarily lie in the same plane, nor are they necessarily perpendicular to crenulation axes. Solutions for the orientation of the crenulation plane, crenulation slip vector, and magnitude of the crenulation slip shear strain belong to one of two possible solution sets, given the orientation of slipping foliation, the foliation slip vector, and the magnitude of slip on foliation. Hence, shear sense may be reliably interpreted from composite planar fabrics in ductile shear zones, but more specifically, shear direction cannot. These results have broad implications in the interpretation of the kinematic significance of mineral lineations oblique to crenulation axes, and in the deduction of shear strain from angular relations between planar fabric elements.