The work deals with numerical simulations of settling or ascension process of a liquid drop in porous media saturated by another liquid. The calculations were carried out using the Darcy model by Level set method with adaptive mesh refinement algorithm that dynamically refines computational mesh near interface. It is shown that the drop is unstable and the finger instability develops at the forefront of moving drop for any ratio of the viscosities of liquids. Under modulated pressure gradient small-scale perturbations of interface are suppressed and in the case of modulation with large enough intensity drop becomes stable.