Hollow fiber membranes offer the opportunity to dramatically reduce the energy required to perform gas separations in the chemical industry. The membranes are fabricated from highly non-Newtonian precursor materials, including concentrated polymer solutions that sometimes also contain dispersed particles. These materials are susceptible to shear-induced microstructural changes during processing, which can affect the characteristics of the resulting membrane. This thesis explores several shear-related effects using materials and flow conditions that are relevant for fiber spinning. The findings are discussed as they relate to membrane processing, and also from the standpoint of enhancing our fundamental understanding of the underlying phenomena. First, the effect of shear on polymeric dope solutions was investigated. Shear-induced demixing—a phenomenon not previously studied in membrane materials—was found to occur in membrane dopes. Phase separation experiments also showed that shear-induced demixing promotes macrovoid formation. The demixing process was found to depend not only on the instantaneous shear conditions, but also on the shear history of the solution. This suggests that low-shear flow processes that occur in the upstream tubing and channels used for fiber spinning can affect macrovoid formation. The effect of viscoelastic media on dispersed particles was also explored. Shear-small-angle light scattering results showed that particles suspended in membrane dope solutions formed aggregated, vorticity-oriented structures when shear rates in the shear-thinning regime of the polymer solution were applied. Shear rates well below the shear-thinning regime did not produce any structure. In fact, the application of a Newtonian shear rate to a sample already containing the vorticity structure caused the sample to return to isotropy. Measurements using a highly elastic, constant-viscosity Boger fluid showed that strong normal forces alone are not sufficient to form the vorticity structures, but that shear thinning is also required. Lastly, a study was conducted examining cross-stream migration of particles dispersed in viscoelastic media. Fluids exhibiting varying degrees of shear thinning and normal forces were found to have different effects on the particle distribution along the shear gradient axis in Poiseuille flow. Shear thinning was found to promote migration toward the channel center, while normal stresses tended to cause migration toward the channel walls. In addition to hollow fiber spinning, many other industrially relevant applications involve polymer solutions and suspensions of particles in viscoelastic media. Often, the properties and performance of the material depend strongly on the internal microstructure. The results from the research described in this thesis can be used to guide the design of materials and processing conditions, so that the desired microstructural characteristics can be achieved.