We present a study of the flux penetration in YBa2Cu3O7−x thin films with a rectangular array of holes (anti-dots), visualizing the magnetic flux density using an advanced magneto-optical technique. Flux penetration patterns are explained by a simple model based on the channeling of vortices along rows of holes. In simulations this was found to lead to a large anisotropy ∼60 of the critical current. However, our experimental anisotropy of 1.30(5) is much smaller. We discuss possible reasons for this discrepancy.