The random trajectory approach derived recently for the purpose of evaluation of the percolation threshold is modified and applied to the modeling of permeability. The main modification consists in probabilistic accounting of possible trajectories, the total permeability being evaluated as a sum over all available percolation trajectories, without any preferences in orientation. Results of calculations of permeability vs porosity, sample thickness, and other structural factors are presented. It is concluded that the qualitative tendencies regarding permeability do not significantly differ from those found before for percolation.