Amyloid fibrillation has been intensively studied because of its association with various neurological disorders. While extensive time-dependent fibrillation experimental data are available and appear similar, few mechanistic models have been developed to unify those results. The aim of this work was to interpret these experimental results via a rigorous mathematical model that incorporates the physical chemistry of nucleation and fibril growth dynamics. A three-stage mechanism consisting of protein misfolding, nucleation, and fibril elongation is proposed and supported by the features of homogeneous fibrillation responses. Estimated by nonlinear least-squares algorithms, the rate constants for nucleation were approximately 10,000,000 times smaller than those for fibril growth. These results, coupled with the positive feedback characteristics of the elongation process, account for the typical sigmoidal behavior during fibrillation. In addition, experiments with different proteins, various initial concentrations, seeding versus nonseeding, and several agitation rates were analyzed with respect to fibrillation using our new model. The wide applicability of the model confirms that fibrillation kinetics may be fairly similar among amyloid proteins and for different environmental factors. Recommendations on further experiments and on the possible use of molecular simulations to determine the desired properties of potential fibrillation inhibitors are offered.