Proteins that perform mechanical functions in living organisms often exhibit exceptionally high strength and elasticity. Recent studies of the unfolding of single protein molecules under mechanical loading showed that their strength is mostly determined by their native topology rather than by thermodynamic stability. To identify the topologies of polymer molecules that maximize their resistance to unfolding, we have simulated the response of cross-linked polymer chains under tensile loading and have found that chain configurations that maximize the unfolding work and force involve parallel strands. Chains with such optimal topologies tend to unfold in an all-or-none fashion, in contrast to randomly cross-linked chains, most of which exhibit low mechanical resistance and tend to unfold sequentially. These findings are consistent with AFM studies and molecular mechanics simulations of the unfolding of beta-sheet proteins. In particular, parallel strands give rise to the high strength of the immunoglobulin-like domains in the muscle protein titin.