We develop a geometrical approach for the relative sliding (shear) between filaments in a bundle subjected to bending and twisting deformations, with applications to motility in flagellated cells. Particular examples for helical and toroidal shapes, and combinations of these, are discussed. The resulting equations for sliding, expressed in terms of the curvature and torsion of filaments, provide conditions for existence of nonlinear internally driven waves along the filament bundle.