The failure of an adhesive layer in a 180degrees peel test is analyzed by the modeling of the peel as an elastica. The adhesive is assumed to fail by a process of cavitation and fibrillation. The resistance of the fibrillated material to deformation gives rise to a rate-dependent peel force F. Governing equations, which take into account the large deformation of the fibrillated materials, are derived. Numerical solutions are obtained for the special case of a linear, viscous adhesive. Assuming a critical strain failure criterion for the fibrils, we show that the peel rate is inversely proportional to the square root of the adhesive thickness and directly proportional to F-3/4. The connection between the peel test and the tack test is also discussed. The maximum traction on the peel arm is found to be directly proportional to the peel force and inversely proportional to the adhesive thickness.