Accurate object shape knowledge provides important information for performing stable grasping and dexterous manipulation. When modeling an object using tactile sensors, touching the object surface at a fixed grid of points can be sample inefficient. In this paper, we present an active touch strategy to efficiently reduce the surface geometry uncertainty by leveraging a probabilistic representation of object surface. In particular, we model the object surface using a Gaussian process and use the associated uncertainty information to efficiently determine the next point to explore. We validate the resulting method for tactile object surface modeling using a real robot to reconstruct multiple, complex object surfaces.