This paper presents novel interaction modes for Model-Based Sonification (MBS) via interactive surfaces. We first discuss possible interactions for MBS on a multi-touch surface. This is followed by a description of the Data Sonogram Sonification and the Growing Neural Gas Sonification Model and their implementation for the multi-touch interface. Modifications from the original sonification models such as the limited space scans are described and discussed with sonification examples. Videos showing interaction examples are provided. Furthermore, the presented system provides a basis for the implementation of known and novel sonification models. We discuss the available interaction modes with multi-touch surfaces and how these interactions can be profitably used to control spatial and non-spatial sonification models.