Introduction Recent work has shown that the transition from persistent to permanent AF in goats coincides with an increase in fibrosis in the outer millimeter of the atrial wall. Macroscopically this leads to reduced electrical conductivity orthogonal to the dominant fiber orientation. A causal relation has not been established yet. Our purpose was to test if epicardial fibrosis can explain the increased incidence of transmural conduction (breakthroughs), which is also observed in permanent AF. Methods We constructed a detailed geometry of the human atria including epicardial layer and all major endocardial bundle structures. The model also includes realistic one to three layers of fiber orientations, corresponding to their location in the atrium. Computer simulations were run with a mesh of 0.2 mm resolution and Courtemanche human atrial cell model. Epicardial fibrosis was modeled by assigning zero transverse conductivity to a random selection of model elements in the epicardial layer. Simulations were performed with 0, 50, and 70% affected elements. Results The numbers of waves, phase singularities, and breakthroughs (BTs) were quantified at different degrees of fibrotic tissue. Increase in the “fibrotic” volume from zero (Control) to moderate (50% Fibrotic), and severe (70% Fibrotic) increased both the number of waves and the number of phase singularities. Along with the increase in fibrosis, the endo-epicardial electrical activity dyssynchrony increased from 8.6% to 18.6%, and 38.4%. Fibrosis increased the incidence of BTs. Conclusion: This model is the first anatomical atrial model to display BTs, a common and conspicuous feature in experimental studies on AF. Epicardial fibrosis in this model increases the degree of endo-epicardial electrical activity dyssynchrony and the incidence of BTs, thus increasing the complexity of fibrillatory conduction. The model offers the opportunity to study transmural conduction, which frequently occurs during AF, in more detail.