Biological protein self-assembly occurs in the cellular milieu, densely occupied by other macromolecules which do not participate directly in the aggregation process. Excluded volume effects arising in such a crowded environment deeply affect the thermodynamics and kinetics of biological processes, like protein folding, ligand binding, and protein aggregation. Here, Langevin dynamics simulations of a simplified model of an amphipathic polypeptide are used to investigate how macromolecular crowding influences the amyloid aggregation kinetics. The simulations show that the net influence of macromolecular crowding on the self-assembly process is the result of two competing effects: oligomer stabilization and solution viscosity increase. Notably, the net effect crucially depends on the aggregation propensity and pathways. Therefore, comparative studies of concentration and crowding effects on the kinetics of amyloid aggregation could shed light on the underlying self-assembly mechanism.