This paper presents the design and implementation of a modular multiphase continuous stirred tank reactor for chemical reaction of polymer fibers.  Chemical reactions on the surface or throughout a thermoplastic fiber present an interesting and challenging reaction engineering problem.  Polymer fiber tows, comprising of 1000-6000 filaments, are functionalized in a series of stirred tank reactors.   The reaction network is quite complex resulting from the intrinsic kinetics in the interior of each filament combined with external mass transfer to the fiber tow surface and intra-filament diffusion.  In the design of this reactor, fundamental reaction engineering principles are applied to address common batch-to-continuous reactor challenges, such as heat and mass transfer, material balances, and reaction kinetics.  The introduction of polymer fibers to a continuous process also requires solution of practical problems associated with fiber processing.  Additional considerations are introduced for designing a reactor system for continuous processing of fiber using liquid with a batch or CSTR contacting pattern in each vessel and containing the effluent gaseous reaction byproducts in a controlled vent stream.