Surface finishing with compliant tools is a widely used technology that still relies heavily on the trial-and-error approach. To predict surface evolution, one should ideally consider the tool as a set of grains and take into account the cutting action of each grain. In practice, the small size of abrasives renders this approach unpractical for industrial application. In this paper, the various aspects playing a role in surface generation, from micro-scale abrasives to macro-scale tool deformation as well as the time-dependent nature of compliant processes, are rationalized and modelled in a Folding Space (FS) rather than a classic geometrical space. This approach drastically reduces the computation time, and is found to be quite realistic as in each position the tool shape is distorted, taking into account the compliance level between the tool and local surface topography. Firstly, the concept of FS and methodology for physical representation of surfaces and processing by compliant tools in the FS are detailed. Next, predictions from the finishing model are analyzed for a variety of compliant grinding and polishing tools typically used in industry. Experimental testing confirms the accuracy and usefulness of the proposed method. To conclude, the model is exploited to offer a better understanding of finishing operations with compliant tools, while the limits and future possibilities of FS simulation method are discussed.