We present computational results concerning the contact line instability as a thin film flows down an inclined plane under gravity. Within the framework of lubrication approximation, we show that the instability and the nature of the pattern formation for a completely wetting fluid strongly depends on the inclination angle. Large inclination angles lead to formation of finger-like rivulets, while smaller angles lead to triangular saw-tooth patterns. However, complete coverage of the substrate by the fluid is always obtained. We also discuss the instability development for long times, and nonlinear mode interaction in large computational domains 1.