Model epoxy networks, with variations in crosslink density and in epoxy monomer rigidity, were prepared to study how the network structure affects modulus, T-g, and toughness/toughenability of epoxy resins. Diglycidyl ether of bisphenol-A and diglycidyl ether of tetramethyl-bisphenol-A, along with the corresponding chain extenders, were chosen to study how monomer backbone rigidity and crosslink density affect physical and mechanical properties of epoxies. The present study indicates that, as expected, the backbone rigidity of the epoxy network, not the crosslink density alone, will strongly influence modulus and T-g of epoxy resins. Upon rubber toughening, it is found that the rigidity of the epoxy backbone and/or the nature of the crosslinking agent utilized are most critical to the toughenability of the epoxy. That is, the well-known correlation between toughenability and the average molecular weight between crosslinks (M-c) does not necessarily hold true when the nature of epoxy backbone molecular mobility is altered. The potential significance of the present findings for a better design of toughened thermosets for structural applications is discussed.