Being able to estimate atrial tissue conductivity parameters from epicardial electrograms is an important tool in diagnosing and treating heart rhythm disorders such as atrial fibrillation. One of these parameters is the atrial fibre direction, which is often assumed to be known in conductivity estimation methods. In this thesis, a novel method to estimate the fibre direction from epicardial electrograms is presented. This method is based on local conduction slowness vectors of a propagating activation wave, which can be calculated from a corresponding activation map of the atrial tissue. These conduction slowness vectors follow an elliptical pattern that strongly depends on the underlying conductivity parameters. The fibre direction and conductivity anisotropy ratio can therefore be estimated by fitting an ellipse to the conduction slowness vectors. Applying the presented method on simulated data shows that it can accurately estimate the fibre direction, and that the performance of the method depends mostly on the range of wavefront directions present in the measurement area. The main advantage of the presented method over existing methods is that it still functions in the presence of conduction blocks, as long as the surrounding tissue is approximately homogeneous.