Prediction of the functional behaviour of precision engineering assemblies requires artificially generated three dimensional rough surfaces that have specific prescribed properties. In this paper, an algorithm is developed for the numerical generation of three dimensional anisotropic rough surfaces that have Gaussian height distribution and a given autocorrelation function with prescribed 3D spatial parameters. The procedure employs the non-linear Conjugate Gradient Method (NCGM) in order to cope with the memory and completing time limitations. The simulated surfaces are compared with those generated by 2-D Digital Filter method. The results show that both the methods can adequately produce rough surfaces at small correlation distances, where as at higher correlation distances, NCGM yields better results.