Many machined surfaces such as those processed by turning, drilling, electrical discharging achining, grinding and rubbing, which have the property of self similarity or self-affinity, can be characterised with fractal geometry. Up to now the emphasis of most researchers has been on isotropic surfaces with a profile of several fractal parameters. In this paper, we first review the characterisation of a profile with fractal geometry and the relation between fractal parameters of the profile and that of a three-dimensional machined surface. Afterward, we propose a concise method based on two-dimensional Fourier transform to compute the surface fractal dimension and to analyse the anisotropy along three-dimensional machined surfaces. The precise three-dimensional topography of a machined surface is taken with atomic force microscopy. After spatial power spectrum obtained by two-dimensional fast Fourier transform, surface fractal parameters are acquired by averaging power spectrum along every direction with nominal same amplitude and anisotropy is analysed according to spectrum amplitude within a certain direction. The results show that this has some advantages over other three-dimensional fractal characterisation methods. It is also obvious this method can be used for either an isotropic surface or an anisotropic one. 2001 Elsevier Science Ltd. All rights reserved.