We systematically investigate the cooperative effects in shear stress relaxation using equilibrium molecular-dynamics simulations in periodic boundary conditions containing a variable degree of strain. We show that, even in simple liquids, shear stress relaxation is a cooperative effect associated with a correlation length that increases with isobaric decrease in temperature. If the system size is less than the correlation length, shear stress in the system is determined by the boundary strain. Transport, however, does not depend on the boundary conditions. We relate these two effects to the number and properties of the configurations accessible to the system. (C) 2004 American Institute of Physics.