The local stability of a cylindrical liquid channel or filament deposited on a planar homogeneous substrate is studied in the framework of an effective interface model including the line tension of the three phase contact line. We discuss the stability with respect to transversally symmetric and antisymmetric deformation modes and compute a stability diagram in terms of the contact angle and the longitudinal wavelength of these modes for different values of line tension. An increase in the line tension always leads to an increase in the local stability of liquid channels or filaments. For large positive line tension, the behaviour with pinned contact lines is recovered. As one decreases the line tension to negative values, deformation modes of arbitrary wavelength destabilize the channel or filament for sufficiently small contact angles. In addition, a negative line tension leads to a band of unstable short wavelength modes within the continuum theory considered here. It is argued that the presence or absence of these latter modes depends on the ratio of the contact line width to the molecular size.