Abstract: A lattice model for fibril formation on the basis of general peptide interactions is presented. Fibrils are well-structured protein aggregates and a key phenomenon in many diseases, among them Alzheimer's disease. We study the model's equilibrium and kinetic properties using Wang-Landau sampling and a Metropolis Monte Carlo algorithm with cluster moves. The peptides are shown to form ordered fibrillar aggregates at low temperatures, while being non-aggregated at high temperatures. A sharp transition separates the two phases. In the kinetic simulations, the growth of fibrils is associated with two lag phases.