In this work, we develop two-dimensional models based on the non-local density functional theory (2D-NLDFT) for the analysis of pore size distribution (PSD) of oxide materials with cylindrical pores with rough and heterogeneous walls. The existing standard NLDFT models for porous oxides assume the smooth energetically uniform surface of the pore walls. Due to this assumption, the calculated theoretical isotherms show typical layering transitions, which are not consistent with the experimental adsorption isotherms measured on real oxide materials. As a result, the fits of standard NLDFT models to N-2 or Ar adsorption isotherms show deviations from the experimental points in association with artifacts observed on the calculated PSD plots. The 2D-NLDFT framework allows us to improve the standard model by introducing the corrugation and energetic heterogeneity to the surface of cylindrical pores. The surface roughness and energetic heterogeneity are known characteristics of the oxide surfaces. With these assumptions we develop a comprehensive approach in which both branches of the adsorption isotherm may be used for the PSD analysis of mesoporous oxide materials. We validate this approach by using Ar data measured at 87 K on the reference set of MCM-41 silica samples (Kruk and Jaroniec, 2000). The generated kernels are smooth, do not show layering transitions and fit accurately the reference data. (C) 2018 Elsevier Inc. All rights reserved.