A method to fabricate multichannel structures based on micrometre-thick plastic foil is described. In a reel-to-reel process, metallized plastic foil is patterned by laser ablation and stacked. Foil-to-foil joints are established by heating the foil stack under pressure. Expansion of the foil stack perpendicular to the plane of the foils yields a multichannel structure. We have realized structures with many thousands of channels with a diameter of a few hundred micrometres. The multichannel structures can serve for mechanical, optical, electrical as well as chemical functions.