Recent experimental measurements of the static and dynamic properties of single fluorescently labeled molecules of DNA in steady shear flow are compared with the predictions of a theoretical model of chain dynamics. The model is based on a set of coupled kinetic equations for the evolution of chain conformations and solvent fluctuations. The polymer is represented as a continuous curve with no excluded volume or hydrodynamic interactions, while the solvent is described by a time and space-varying velocity field. In the absence of constraints that enforce the finite extensibility of the chain at large shear rates, the calculated curves of the normalized dynamic autocorrelation function of the mean extension reproduce the qualitative features of the measured curves, but otherwise deviate significantly from them. We develop an analytically tractable finitely extensible model of the Gaussian chain that is more successful in reproducing the experimental data.