The dynamics of individual Deoxyribonucleic acid (DNA) molecules in semidilute solutions undergoing planar extensional flow is simulated using a multiparticle Brownian dynamics algorithm, which incorporates hydrodynamic and excluded volume interactions in the context of a coarse-grained bead-spring chain model for DNA. The successive fine-graining protocol [P. Sunthar and J. R. Prakash, Macromolecules 38, 617–640 (2005); R. Prabhakar et al., J. Rheol. 48, 1251–1278 (2004)], in which simulation data acquired for bead-spring chains with increasing values of the number of beads Nb, is extrapolated to the number of Kuhn steps NK in DNA (while keeping key physical parameters invariant), is used to obtain parameter-free predictions for a range of Weissenberg numbers and Hencky strain units. A systematic comparison of simulation predictions is carried out with the experimental observations of Hsiao et al. [J. Rheol. (in press)], who have recently used single molecule techniques to investigate the dynamics of dilute and semidilute solutions of k-phage DNA in planar extensional flow. In particular, they examine the response of individual chains to step-strain deformation followed by cessation of flow, thereby capturing both chain stretch and relaxation in a single experiment. The successive fine-graining technique is shown to lead to quantitatively accurate predictions of the experimental observations in the stretching and relaxation phases. Additionally, the transient chain stretch following a step strain deformation is shown to be much smaller in semidilute solutions than in dilute solutions, in agreement with experimental observations.