A three-dimensional model and its support structure are built by fused deposition modeling techniques, wherein a thermoplastic material containing silicone is used to form the support structure and/or the model. The thermoplastic material containing silicone exhibits good thermal stability, and resists build-up in the nozzle of an extrusion head or jetting head of a three-dimensional modeling apparatus. The silicone contained in a support material acts as a release agent to facilitate removal of the support structure from the model after its completion.