Haptic rendering is an important area of research that enables the user to employ haptic perception in human-computer interaction. An important motivation here is to use the human touch to study the behavior of various models. However, the high refresh rate needed for a stable haptic interaction on the one hand and the high-computational-cost characteristic for the simulation of numerous phenomena on the other hand represent a big issue. In this paper, an approach based on the distributed construction of configuration spaces is presented. The main idea behind this approach is to profit from employing a high-performance environment (e.g., computational grid) to overcome or at least moderate the high-frequency issue. The approach is presented using nonlinear deformation models, which are essential for realistic modeling of soft tissues. A distributed algorithm is presented, and its properties are evaluated quantitatively.