The breakup of a thin non-evaporating liquid film that is either flowing down or climbing on a vertical or inclined surface and subject to cocurrent or countercurrent interfacial shear (or gas flow) is investigated analytically. Analytical expressions for the dimensionless liquid film thickness, $\Delta_{\hbox{\scriptsize\it min}}$, and wetting rate, $\Gamma_{\hbox{\scriptsize\it min}}$, at breakup are derived based on the minimization of the total energy of a stable rivulet, formed following the film breakup. For a downflowing liquid film, increasing the cocurrent interfacial shear (or gas velocity) or decreasing the equilibrium contact angle, $\theta_{o}$, decreases both $\Delta_{\hbox{\scriptsize\it min}}$ and $\Gamma _{\hbox{\scriptsize\it min}}$, below their values with zero interfacial shear. Conversely, increasing the countercurrent interfacial shear or $\theta_{o}$, increases both $\Delta_{\hbox{\scriptsize\it min}}$ and $\Gamma_{\hbox{\scriptsize\it min}}$, above their values with zero interfacial shear. The predictions of $\Delta _{\hbox{\scriptsize\it min}}$ and $\Gamma _{\hbox{\scriptsize\it min}}$ for a climbing water film on a vertical surface are in good agreement with reported experimental data for a wide range of cocurrent gas velocities.