Abstract: In the paper it is found by a theoretical analysis and numerical experiments that the bifurcation of unstable interface between fluids in porous medium can be determined essentially by the values of dimensionless parameters C1 and 5. For any given C1 there is a critical value S1 of 5 such that when 1 < 5 < S1 the flat interface perturbed by any small disturbance will develop to a long finger without bifurcation. There is a critical value C1* of C1 such that for any given C1 > C1* there are two distinct crit...