Shear banding is a type of plastic flow instability with often adverse implications for cutting and deformation processing of metals. Here, we study the mechanics of plastic flow evolution within single shear bands in Ti- and Ni-based alloy systems. The local shear band displacement profiles are quantitatively mapped at high resolution using a special micromarker technique. The results show that shear bands, once nucleated, evolve by a universal viscous sliding mechanism that is independent of microstructural details. The evolution of local deformation around the band is accurately captured by a momentum diffusion equation based on a Bingham-type flow rule. The predicted band viscosity is very small, compared to those of liquid metals. A plausible explanation for this small viscosity and fluid-like behavior at the band, based on phonon drag, is presented.