We present the effect of confining walls on the theology and dynamics of dilute polymeric solutions using a self-consistent multiscale simulation technique. In Part I we formulate the mathematical problem necessary to understand and model these dynamics. Various polymer models (the Kramers' freely jointed bead-rod chain, FENE, worm-like, and inverse Langevin chains) are used to describe the polymer chain dynamics based on their success in previous studies [H.P. Babcock et al., Phys. Rev. Lett. 85, 2018 (2000); J. S. Hur et al., J. Rheol. 44, 713 (2000); 45, 421 (2001)]. Theoretical arguments suggest that the main consequences of confinement on chains are (a) the entropic force law is altered due to the loss of chain configurational space and (b) the viscous drag on the chain is increased due to hydrodynamic interactions with the wall. In this study, the correct entropic spring force law in the presence of confining walls is developed. In addition, an efficient multiscale simulation technique for modeling the dynamics of bead-spring models with the force law is reported. (C) 2004 The Society of Rheology.