In the recent past, data-driven approaches have gained importance for modeling and rendering of haptic properties of deformable objects. In this paper, we propose a new data-driven approach based on a well known machine learning technique: random forest. We train the random forest for regression for estimating the input-output mapping between discrete-time interaction data (position/displacement and force) collected on a homogeneous deformable object. Unlike currently existing data-driven approaches, we use at most 1% of the recorded interaction data for the training of the random forest. Even then, the trained random forest model reproduces all the interactions used for the training with a good accuracy. This also provides promising results on unseen data. When employed for haptic rendering, the model estimates smooth and stable interaction forces at an update rate more than 650 Hz.