In this three part study, nonequilibrium molecular dynamics simulation of the rheology of confined films is used to explore the microscopic properties and response of model lubricants under shear. The rheological behavior of two alkanes that differ in molecular structural complexity is examined: tetracosane (C24H50), which is a linear alkane, and squalane (C30H62), which has six symmetrically placed methyl branches along a 24 carbon backbone. The model lubricants are confined between model walls that have short chains tethered to them, thus screening the wall details. Shear flow is generated by moving the walls at constant velocity, and various properties are calculated after attainment of steady state, Heat generated by viscous dissipation is removed by thermostatting the first two atoms of the tethered molecules at 300 K, which allows a temperature profile to develop across the width of the lubricant layer, This paper details the molecular model and simulation method, and examines interfacial slip al the interface between the tethered chains and the fluid alkane, The effects of various parameters on the slip behavior are presented. Two subsequent papers respectively address the structural features of these liquid alkanes under shear flow: and compare the viscosities from independent calculations of the bulk and confined fluids. (C) 1997 American Institute of Physics. [S0021-9606(97)50847-6].