An instrument modification to a capillary extrusion rheometer is described which permits ready measurement of the viscosity‐shear rate behavior of concentrated polymer solutions, particularly in the generally inaccessible region of high temperatures with volatile solvents. Despite the fundamental rheological and practical commercial importance of defining the viscosity behavior of highly concentrated (e.g., 50–100%) polymer solutions at temperatures well above the solutionTg,few data in this region are available in the literature. This is largely because of the experimental difficulty of making measurements in the concentrated solution region under conditions where significant evaporative solvent losses are likely to occur. Instrumentation and methodology for performing these experiments with relative ease and generally good precision are described, and typical viscosity‐shear rate curves obtained for solutions of polystyrene in ethylbenzene at various concentrations (50–90 wt %) and temperatures (100–225°C) are reported to demonstrate the method.