This work presents a cooperative, force-based handling approach for the lay-up of highly deformable materials on a mold, a scenario, e. g., encountered during the manufacturing of fiber reinforced plastics. A two-dimensional preforming demonstrator is designed which reflects the basic functionality of the process under consideration. Suitable mathematical models of the demonstrator and the deformable material provide a basis for the controller design and a force-based motion planning framework for the lay-up process. The framework proves to be most flexible as it does not rely on preplanned position trajectories but calculates the movements of all manipulators on-line and can promptly react to external disturbances. Experimental results on the demonstrator underline the feasibility and performance of the presented approach for the lay-up of a deformable fabric on a double-curvature mold.