In spite of the development of automated tolerance inspection systems for manufactured parts over the years, there are still processes that inevitably require manual intervention making full automation impossible in most cases; in particular when dealing with deformable parts. In most current industrial inspection systems, a deformable part under inspection must first be mechanically constrained on a rigid support or jig so as to be able to compare it with its nominal shape. This paper presents a new system to perform real-time surface inspection of deformable parts that does not require fixturing. Instead, the proposed system applies virtual forces to the part’s CAD model as if the part was installed in the fixturing device. Normally, a precise finite element method (FEM) simulation should be used to approximate the deformation that appends when the part is installed in the device. Even with a fast parallel computer, FEM is far from being real-time and cannot be used for on-line inspection. In the proposed system, a radial basis function approximation of the FEM simulation is trained off-line and used to speed-up the simulation by an order of magnitude. Experimental evaluation of the proposed system is presented for three plastic parts. Using the proposed scheme, an approximation of 0.25 mm compared with the real deformation was obtained. In this paper, statistical results are presented such as the average deviation, standard deviation, and processing time between the approximations obtained with the proposed method and with the finite element method applied to the full CAD model.