Boring bars with tuned mass dampers have a passive damper tuned with respect to the frequency of the first bending mode of the tool. When the tool is clamped into the machine tool there is a stiffness loss that lowers the natural frequency of the bar compared to ideal clamping conditions. For large tools the difference can be more than 35%, depending on clamping structure, tool size and overhang. In this paper we investigate a simple two-degree-of-freedom model for the tool-machine interaction consisting of a bending mode coupled with a rotational stiff mode. The model gives good insight into the system behavior and fits well with measurements. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of The 17th CIRP Conference on Modelling of Machining Operations