This paper attempts to provide a theoretical basis for the use of Dissipative Particle Dynamics (DPD) in the area of viscoelastic flow modelling. To generate elasticity in the DPD base fluid, an extension of the DPD simulation model is proposed. The extension consists of assigning to each DPD particle a polymer strand end-to-end vector. The standard DPD evolution and interaction rules are likewise extended. By aid of kinetic theory, it is shown that the ensuing fluid dynamics is equivalent to the Navier-Stokes equation supplemented with a polymeric stress contribution. For specific choices of the evolution and interaction rules for the end-to-end vector the polymeric stress contribution can be put into correspondence with standard models, such as the Hookean dumbbell model.