In living cells, the cytoskeleton connects to the extracellular environment through focal adhesions, multimolecular structures that can sense applied force. A model is presented that for the first time explains why the focal adhesions tend to high-curvature regions at the cell periphery. It is based on experimental evidence for positive feedback between adhesion formation and assembly of actomyosin bundles (stress fibers). The model predicts that the focal adhesions propagate by treadmilling with a velocity proportional to the integrin diffusion coefficient.