Measurements of the force required for the pull-off of N polyvinylsiloxane fibrils from glass surfaces reveal that it varies linearly with the total contact perimeter, NS. This finding cannot be rationalized using existing models of adhesion. A new model is introduced which exploits the analogy with rupture of brittle solids; it proposes that fibril detachment under tension is controlled by weakest link defects. The model predicts a power law dependence of the force; i.e., NSn with exponent n varying between 1 and 2. The linear dependence found experimentally arises when the defects are present with broad size dispersion.