We report results of Brownian dynamics simulations of the steady state and transient rheological behavior of bead and spring chain models in elongational flow. The simulations include examination of the effects of excluded volume, hydrodynamic interactions, chain length, and maximum bond extension. Hydrodynamic interactions are modeled by the Rotne–Prager–Yamakawa tensor. The steady state results for the rheological properties of finitely extensible nonlinear elastic (FENE) chains in the absence of hydrodynamic interactions and excluded volume interactions are compared with the analytic FENE‐PM theory of Wedgewood and co‐workers. For bead and spring models with short bond lengths, excluded volume and hydrodynamic interactions are shown to affect the steady state rheological properties significantly.