We suggest a physical mechanism by which antimicrobial peptides spontaneously induce stable pores in membranes. Peptide binding to a lipid bilayer causes an internal stress, or internal membrane tension, that can be sufficiently strong to create pores. Like detergents, peptides have a high affinity for the rim of the pore. Binding to the rims reduces the line tension and decreases the number of peptides causing the internal membrane tension. Consequently, the pore radius is stable. The pore formation resembles a phase transition.