The study is dedicated to catalysts on the base glass microfibrous supports. It discusses the issues of the diffusion of reactants in the bulk of glass fibers, using the model reaction of toluene deep oxidation in air at Pt-containing glass-fiber catalyst (GFC). The catalysts with location of Pt particles either at the external fiber surface or in the hypothetical sub-surface layers in the glass bulk are compared. The intra-fiber diffusion of toluene is considered from positions of diffusion in liquid, interpreting glass as super-cooled liquid with high viscosity. The calculations show that at moderate temperatures the diffusion coefficient and corresponding efficiency factor are extremely low due to very high viscosity of high-silica glasses. The apparent reaction rate at sub-surface Pt particles appears to be dramatically lower (by 7-10 orders of magnitude) than that for the surface Pt. It is concluded that even if the sub-surface metal particles really exist, their contribution to the overall performance of GFC is negligible. This result disproves the notion stating that properties of some class of GFCs are defined by subsurface particles of active component.