  Zero modes of various matters with spin 0, 1 and 1/2 on a class of scalar
flat thick branes are discussed in this paper. We show that scalar field with
spin 0 is localized on all thick branes without additional condition, while
spin 1 vector field is not localized. In addition, for spin 1/2 fermionic
field, the zero mode is localized on the branes under certain conditions.
