Linear stability analysis is applied to the Richards equation by perturbing the pressure field. An analytical solution of the stability problem of flow through stratified media is presented. It is obtained under two simplifying assumptions: the quasi-steady hypothesis and the quasi-linear hypothesis. Flow is found to be unconditionally stable. A numerical experiment and the comparison with published data supports the conclusion that upscaling capillary phenomena is crucial in order to capture the essence of finger flow by continuum models.