Plasma momentum transport within magnetic surfaces plays a fundamental role in a number of toroidal plasma physics issues, such as turbulence suppression, impurity transport, bootstrap current generation and the shielding of resonant magnetic error field perturbations. Stellarators provide opportunities for improved understanding of plasma flow effects because (a) new forms of quasi-symmetry (e.g. helical, poloidal) can be produced that differ significantly from the tokamak and (b) symmetry-breaking effects (always present to some degree) reduce the close coupling between parallel and cross-field transport characteristics of symmetric systems. External control coils can also be used to further enhance or suppress such effects. A method has been developed to evaluate the variation of neoclassical self-generated plasma flows in stellarators both within and across magnetic surfaces. This introduces a new dimension into both the optimization of stellarators and to the improved understanding of the existing confinement database. Application of this model to a range of configurations indicates that flow directionality and shearing rates are significantly influenced by the magnetic structure. In addition, it is demonstrated that flows in stellarators are sensitive to profile effects and the presence of external momentum sources, such as neutral beams.