A novel method of investigating the link between molecular features of polymer molecules and the rheological properties of dilute polymer solutions has been investigated. It applies the dissipative particle dynamics (DPD) computer simulation technique, which introduces a lattice‐gas automata time‐stepping procedure into a molecular‐dynamics scheme, to model bead‐and‐spring‐type representations of polymer chains. Investigations of static and dynamic scaling relationships show that the scaling of radius of gyration and relaxation time with the number of beads are consistent with the predictions of the Rouse–Zimm model. Both hydrodynamic interaction and excluded volume emerge naturally from the DPD polymer model, indicating that a realistic description of the dynamics of a dilute polymer solution can be obtained within this framework, and that very efficient computer simulations are possible.