When fibrillation occurs during peeling, the normal stress in the adhesive may gradually reduce to zero at the peel front. The shear stress also reduces to zero. Classical beam-spring (or beam-on-elastic-foundation) models do not yield solutions that have these properties. With the use of a beam-on-foundation model combined with a cohesive zone in the neighborhood of the peel front, these properties can be satisfied. In order to obtain analytical solutions, peel tests are considered in which the backing has a small slope and is linearly elastic in the adhered region, and the traction law is assumed to be piecewise linear. Cases are considered with only normal stresses in the adhesive (mode I), only shear stresses (mode II), and both stresses coupled (mixed-mode behavior). Analytical solutions are obtained for displacements of the backing, forces in the backing, and stresses between the adhesive and the backing.