Brownian dynamics simulation is used to investigate the viscoelastic response of the Gaussian chain to a step shear deformation in both the linear and non-linear regions under the influence of hydrodynamic interactions. Both the preaveraged Oseen tensor and the Rotne-Prager tensor are used in the study. In the former case, the simulation results are shown to be in agreement with the expected results calculated using the eigenvalues of the normal modes of motion obtained numerically. It is shown that an initial state with zero second normal-stress difference is generated by the step shear deformation. The subsequent rise of the second normal-stress difference as revealed by the simulation is shown mainly arising from the coupling of the recoil of the stretched bond in the direction of deformation and the anisotropy in the hydrodynamic interaction created by the step deformation. (C) 2003 Elsevier Science Ltd. All rights reserved.