We present a three-dimensional (3D) model for adhesion enhancement due to crack trapping in a film-terminated fibrillar structure. Adhesion enhancement occurs due to trapping of the interfacial crack in the region between fibrils. Energy release to the crack tip is attenuated because, between fibrils, it has to pass through the compliant terminal film. Using perturbation theory and a finite element method, we solve for the shape of crack front, which is unknown. Our model thus also allows us to study how adhesion enhancement depends on the arrangement of fibrils. For example, our model explains why, for a fixed area density of fibrils and for similar crack orientations, hexagonal arrays have higher adhesion than square arrays. (C) 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2368-2384, 2009