A lattice model is presented for the simulation of dynamics in polymeric systems. Each polymer is represented as a chain of monomers, residing on a sequence of nearest-neighbor sites of a face-centered-cubic lattice. The polymers are self- and mutually avoiding walks: no lattice site is visited by more than one polymer, nor revisited by the same polymer after leaving it. The dynamics occurs through single-monomer displacements over one lattice spacing. To demonstrate the high computational efficiency of the model, we simulate a dense binary polymer mixture with repelling nearest-neighbor interactions between the two types of polymers, and observe the phase separation over a long period of time. The simulations consist of a total of 46 080 polymers, 100 monomers each, on a lattice with 13 824 000 sites, and an interaction strength of 0.1k(B)T. In the final two decades of time, the domain-growth is found to be d(t)similar tot(1/3), as expected, since the lattice model shows the dynamical scaling of "Model B," once the domains are bigger than the radius of gyration. (C) 2003 American Institute of Physics.