Amyloid-β (Aβ) peptides can elongate in the fibril axis and associate in the lateral direction. We present detailed atomic Aβ models with different in-register intermolecular β-sheet-β-sheet associations. We probe structural stability, conformational dynamics, and association force of Aβ oligomers with various sizes and structures for both wild-type and mutated sequences using molecular dynamics (MD) simulations. MD simulations show that an Aβ oligomer that is laterally associated through the C-terminal-C-terminal interface is energetically more favorable than other oligomers with the N-terminal-N-terminal and C-terminal-N-terminal interfaces. We further develop a simple numerical model to describe the kinetics of Aβ aggregation process by considering fibril elongation and lateral association using a Monte Carlo algorithm. Kinetic data suggest that fibril elongation and lateral association are mutually competitive. Single-point mutations of Glu22 or Met35 at the interfaces have profound negative effects on intermolecular β-sheet-β-sheet association. These disease-related mutants (E22K, E22Q, and M35O) display more flexible structures, weaker lateral association, and stronger elongation tendencies than the wild type, suggesting that amyloid oligomerization and neurotoxicity might be linked to fibril longitudinal growth.