Three-dimensional surface roughness of mating parts of engineering assemblies has a significant influence on their functional behaviour. Studies on load bearing capacity in elastohydrodynamic contacts, gap flow analysis in precision hydraulic assemblies using modeled 3D fluid continuum micro gap geometry, etc., have made it possible to quantify the effect of certain 3D surface roughness parameters on frictional behaviour of the assemblies. This set forth the need for artificially generated three-dimensional engineering surfaces having prescribed roughness values for a better understanding and prediction of tribological problems. In this paper, an algorithm is developed for the numerical generation of three-dimensional anisotropic surfaces with prescribed 3D surface roughness parameters. The procedures employ either the Non-linear Conjugate Gradient Method (NCGM) or 2-D Digital Filter method. The results show that both the methods can adequately produce surfaces at small correlation distances, while at higher correlation distances the NCGM yields better results. Comparison between model-simulated output and measurement results of three-dimensional surface roughness of engineering surface show a good match, supporting the validity of the model. © 2010 Elsevier B.V. All rights reserved.