Falling films on inclined planes display surface and shear instability modes, the latter being important at small angles &bgr; of inclination of the plane. These modes are analyzed with particular attention paid to the effects of surface tension. The results show that the critical Reynolds number of the shear mode is nonmonotonic in either the angle &bgr; or the surface‐tension parameter &zgr; but displays a local minimum at nonzero values of &bgr; and &zgr;. For large Reynolds number, an analysis shows that the shear mode is inviscidly stable, but that the surface mode is unstable.