A "sheath" fluid passing through a microfluidic channel at low Reynolds number can be directed around another "core" stream and used to dictate the shape as well as the diameter of a core stream. Grooves in the top and bottom of a microfluidic channel were designed to direct the sheath fluid and shape the core fluid. By matching the viscosity and hydrophilicity of the sheath and core fluids, the interfacial effects are minimized and complex fluid shapes can be formed. Controlling the relative flow rates of the sheath and core fluids determines the cross-sectional area of the core fluid. Fibers have been produced with sizes ranging from 300 nm to ~1 mm, and fiber cross-sections can be round, flat, square, or complex as in the case with double anchor fibers. Polymerization of the core fluid downstream from the shaping region solidifies the fibers. Photoinitiated click chemistries are well suited for rapid polymerization of the core fluid by irradiation with ultraviolet light. Fibers with a wide variety of shapes have been produced from a list of polymers including liquid crystals, poly(methylmethacrylate), thiol-ene and thiol-yne resins, polyethylene glycol, and hydrogel derivatives. Minimal shear during the shaping process and mild polymerization conditions also makes the fabrication process well suited for encapsulation of cells and other biological components.