Numerical simulations and experimental study of incompressible Newtonian permeate flow in porous support of hexagonal 19-channel inorganic membrane are presented both for filtration and backflush operating modes. Under several simplifying assumptions the problem could be treated as two-dimensional potential flow. The mathematical model was solved using finite element method. The results of numerical simulations show that the contributions of particular channels to the total permeate flux are not equal and depend on the ratio of skin layer to porous support permeability as well as on the distance of a channel from the membrane outer surface. For membranes with high permeability of skin layer there is an area of nearly constant pressure around inner channels and their contribution to total flux is negligible. This effect will probably be more pronounced in backflush operating mode while in filtration mode possible dynamic membrane adds a resistance to that of skin layer which leads to more uniform permeate flux distribution. Qualitative trends of the numerical simulations were verified by experiments with ceramic 19-channel membranes of Membralox(R) type in backflush operating mode.