In the calculation of complex flows of non‐Newtonian fluids, fundamental difficulties with the existence of solutions and the convergence of numerical methods arise as a consequence of using one‐particle constitutive equations in which the stress (or extra‐stress) tensor in a fluid element is not affected by the stress and strain histories of neighboring material. For that reason, we formulate here a class of multiparticle constitutive equations based on the idea of polymer diffusion for which one expects that the above‐mentioned difficulties are avoided. The very general ideas are developed in the body tensor formulation of constitutive equations, and the modifications resulting for Maxwell, Oldroyd‐A/B, and K‐BKZ models are described explicitly. Application of the modified models in the numerical solution of non‐Newtonian flow problems is straightforward.