Three kinetic theory models are used to predict the spatiotemporal stress and velocity fields that arise in the startup of Couette flow. The models considered do not have analytic closed-form expressions for the stress tenser. Nevertheless, using a combined finite-element and Brownian dynamics technique (CONNFFESSIT), numerical solutions can be found. To describe the dynamics for dilute polymer solutions, a dumbbell model with finite extensibility, internal viscosity and hydrodynamic interaction is considered. Polymer melts are described by a reptation model that does not assume independent alignment or consistent averaging, and liquid crystals are considered using Doi and Edwards’ model without consistent averaging. The three examples show how simple kinetic theory ideas on the microscopic scale can predict very different, but qualitatively reasonable, macroscopic flow fields in non-homogeneous flows, hence cannot be solved by strictly continuum-mechanical methods.