This paper reviews the existing numerical analysis methods and their problems in surface metrology. Based on the requirements of functional analysis of surfaces, this paper proposes a lifting wavelet representation for extraction of different components of a surface. The theory of the lifting wavelet is introduced and a fast algorithm is developed. Different frequency components of the surface can be separated, extracted and then reconstructed according the intended requirements of functional analysis. The surface textures can be highlighted and multi–scalar topographical features can be identified and clearly recovered. In order to verify the behaviour of the new model, a computer simulation based on sinusoidal and triangular waveforms is used. Case studies are conducted using a series of typical surfaces of engineering and bioengineering, such as planes, cylinders and curves, measured by contact (stylus) and non–contact (phase–shifting interferometry) instruments, to demonstrate the feasibility and applicability of using the lifting wavelet model in the analysis of these surfaces.