A long, flexible polymer molecule consists of hundreds of thousands of monomeric units. Detailed atomistic simulation of such a molecule and surrounding solvent molecules is not practical if one is interested in detailing the molecule’s dynamics. We could model the chain as a continuous curve of a certain atomic thickness, where the forces mediated through the surrounding solvent molecules are incorporated as hydrodynamic interactions. However, computer simulation of such a model demands a level of discretisation, which usually involves postulation of bead-spring (or pearl-necklace) models where hydrodynamic interactions are prescribed between spherical beads of fixed radii. This leads to an additional modelling parameter and is unable to accurately model dynamics of highly stretched chains without fine- (as opposed to coarse-) graining. In 2006-07 we developed a scheme for coarse–graining hydrodynamic interactions where the chain is represented by a series of orientable and stretchable Gaussian blobs, with no additional tuning parameters. We constructed Brownian dynamics simulations of the relaxation of strongly stretched chains, modelled with the new scheme, and demonstrated that the transient radius of gyration and first normal stress difference are less sensitive to the degree of coarse graining than the conventional bead-spring model with RPY hydrodynamic interactions.