This paper has extended a lattice Monte Carlo (MC) method to simulate the simple shear flow of multiple self-avoiding chains in three dimensions following our research work in two dimensions. Comparisons of simulation outputs with experimental observations, theoretical predictions and other simulation results are made. The steady-stare scaling analysis to scattering functions of deformed chains confirms the existence of anisotropic scaling laws at fixed reduced shear rates found in molecular dynamics (MD) simulation. The exponent of chain deformation shown in the MC simulation falls into a normal regime measured from neutron scattering and light scattering experiments. The relation between orientation angles and shear rates is consistent with some scattering experiments. Both Newtonian and non-Newtonian regimes are reproduced in our lattice MC simulation. Non-zero first and second normal stress differences and their dependence of the shear rate are found, as well as the shear thinning effect. The stress growth at inception and stress decay after cessation of shear flow is also examined. The validity of our novel simulation approach is thus confirmed. Since both chain conformations and rheological properties under shear flow can be studied, our MC approach can be used to reveal non-linear viscoelasticity of polymer fluids and polymer-flow interaction. (C) 2000 Elsevier Science Ltd. All rights reserved.