Tangibles on interactive surfaces enable users to physically manipulate digital content by placing, manipulating, or removing a tangible object. However, the information whether and how a user grasps these objects has not been mapped out for tangibles on interactive surfaces so far. Based on Buxton’s Three-State Model for graphical input, we present an interaction model that describes input on tangibles that are aware of the user’s grasp. We present two examples showing how the user benefits from this extended interaction model. Furthermore, we show how the interaction with other existing tangibles for interactive tabletops can be modeled.