Cadherins are a family of proteins responsible for intercellular adhesion between epithelial cells and for maintaining tissue integrity. E-cadherin, found in adherens junctions, and desmogleins and desmocollins, found in desmosomes, are three classical-type cadherins that interact through their extracellular domains. These have five extracellular cadherin (EC) repeats that link adjacent cells through a tip-to-tip interaction mediated by an exchange of conserved tryptophans in their distal extracellular repeats. Here we present large-scale molecular dynamics simulations that model the complete extracellular domains of available crystal structures, with systems encompassing up to 5 million atoms. Equilibrium and steered molecular dynamics simulations of E-cadherin lattices predict a two-phase elastic response in which E-cadherin complexes first straighten and then unbind without unfolding. Cis-interactions are predicted to play a minor role in the mechanical response of these complexes. Simulations of the desmoglein/desmocollin systems show that forces required to unbind both the homodimer of desmoglein-2 and a canonical heterodimer of desmoglein-2 and desmocollin-1 are similar, even in the presence of a salt-bridge shown to be important for the heterodimer interaction. As with the E-cadherin system, both the desmoglein dimer and desmoglein/desmocollin systems exhibited unbinding after an initial straightening of both molecules, with no unfolding. Overall, our simulations provide insights into the molecular mechanics of adherens junctions and desmosomes.