The structural and dynamic properties of polymers, with excluded volume interactions, in simple shear flow, are investigated by a Monte-Carlo algorithm. Chain lengths of 5, 100 and 150 beads have been studied. For middle-sized polymers (100 or 150 beads), in strong shear, after the polymers have reached maximum elongation, beyond a shear rate threshold, the rear back of the polymer chains begins to fold and to spiral, in the wake of the running elongated polymer head. The potential part of the polymer＇s shear viscosity is evaluated at different shear rates, using non-equilibrium Monte-Carlo simulation. In spite of large statistical fluctuations of the shear viscosity computations, simulations for middle-sized polymers (100 or 150 beads) show a shear thinning behaviour. The simulation results should be compared with experiments.