A modeling apparatus includes a platform and a substrate, which are adapted to be releasably locked together to provide a surface for building up models in an additive-process three-dimensional modeling machine. The substrate comprises a substantially rigid, non-dusting tray providing a modeling surface. Male connectors extending from the tray are seated in female connectors in the platform, to engage the substrate to the platform. The engaged substrate is locked to the platform, maintaining accurate positioning of the substrate while a model is built. After modeling is complete, the substrate is released from the platform, the model is removed, and the substrate may be reused.