Brownian dynamics simulations are used to predict the evolution of DNA conformations in elongational flow. The DNA molecule is represented by a bead-spring chain model, and excluded-volume and hydrodynamic interactions between the beads are taken into account. Two distinct types of behavior are examined, corresponding to infinite and finite chains. In the former case, Hookean springs are used, and simulations data accumulated for chains with increasing numbers of beads, N, are extrapolated to the limit N --> infinity. In this nondraining limit, universal DNA stretch vs strain curves are obtained as a function of the solvent quality parameter z. In the case of finite chains with N-k Kuhn steps, finitely extensible springs are used, and the extrapolation of finite chain data is restricted to the limit (N - 1) --> N-k. It is shown that in the presence of finitely extensible springs both the excluded-volume and hydrodynamic interaction parameters need to be redefined appropriately. The role of finite size effects and sensitivity to the choice of parameter values is examined by comparing the finite chain stretch vs strain curves with the universal curves. Theoretical predictions are also shown to compare favorably with experimental observations of DNA stretch.