The replication casting process is used for manufacturing open-pore aluminum foams with advanced performances, such as stability and repeatability of foam structure with porosity over 60%. A simple foam structure model based on the interaction between sodium chloride solid particles poorly wetted by melted aluminum, which leads to the formation of air pockets (or “air collars”), is proposed for the permeability of porous material. The equation for the minimum pore radius of replicated aluminum foam is derived. According to the proposed model, the main assumption of the permeability model consists in a concentration of flow resistance in a circular aperture of radius r min. The permeability of aluminum open-pore foams is measured using transformer oil as the fluid, changing the fractions of initial sodium chloride. Measured values of minimum pore size are close to theoretically predicted ones regardless of the particle shape. The expression for the permeability of replicated aluminum foam derived on the basis of the “bottleneck” model of porous media agrees well with the experimental data. The obtained data can be applied for commercial filter cells and pneumatic silencers.