Using a polymeric model, we study via Monte Carlo simulation the structure and stability of an amphiphilic bilayer against pore formation. The simulations yield the absorption isotherm of the amphiphile in solution. At a critical micelle concentration around 1.5x10(-3), a bilayer forms, and the composition and orientation profiles across it are obtained. The bilayer tension is estimated via the spectrum of undulations. Pores in the bilayer are caused to nucleate by reducing the chemical potential of the amphiphile, and small ones form by peristaltic fluctuations of the bilayer thickness. In large pores, the amphiphile heads rearrange so as to shield the tails from solution. Composition profiles across pores of various sizes are obtained. An effective edge tension is extracted from the distribution of sizes and agrees with a simple model of a hydrophilic pore.