A fiber includes one or more layers of polymer surrounding a central lumen, and living animal cells disposed within the lumen and/or within at least one of the one or more layers, wherein the fiber has an outer diameter of between 5 and 8000 microns and wherein each individual layer of polymer has a thickness of between 0.1 and 250 microns. Also disclosed are model tissues including such fibers, and method of making such fibers. The fibers can serve as synthetic blood vessels, ducts, or nerves.