A potential model for cylindrical pores with Lennard-Jones (U) wall-fluid interaction is of importance for modeling porous materials in adsorption and catalysis. In this work, we derived a complete analytical potential model. In derivation the interaction energy between the LJ cylindrical wall-fluid is integrated by transforming the integrals into the elliptic ones. A simple expression containing the hypergeometric function is obtained without any approximation and numerical integration. The model is compared with three existing models. It gives exactly the same potential energy as the model of Peterson et al. However, inconvenient numerical integration in their model is avoided here. When the wall thickness decreases to insignificant, our model is reduced to the model of Tjatjopoulos et al. derived from a surface wall. Compared with the simplified model proposed by this group previously, this model is more accurate for not introducing any approximation. To explore the effect of the potential models on adsorption, we used grand canonical Monte Carlo (GCMC) method to simulate isotherms for an LJ fluid, whose parameters are taken from the literature for nitrogen molecule, in an LJ cylindrical pore of diameter 3.5 nm and thickness 0.35 nm. It is found that the adsorption isotherms are sensitive to the potential models. In summary, the model proposed can be easily applied to computer simulation and density functional theory calculation of the LJ wall-fluid interaction for cylindrical pores of finite wall thicknesses. (C) 2004 Elsevier B.V. All rights reserved.