  This work focuses on an unexplored aspect of non-symmetric geometry where
{\it only} the off-diagonal metric components along the extra dimension, in a
5-dimensional spacetime, are non-symmetric. We show that the energy densities
of the stationary non-symmetric models are similar to that of brane models
thereby mimicking the thick-brane scenario. We find that the massive test
particles are confined near the location of the brane for both growing and
decaying warp factors. This feature is unique to the non-symmetric nature of
our model. We have also studied the dynamical models where standard 4D FLRW
brane is embedded. Our analysis shows that the non-symmetric terms deconfine
energy density at the early universe while automatically confine at late times.
