  We provide the cosmological solutions for Randall-Sundrum models with the
bulk energy-momentum $\hat T^5_5$ incorporated. It alters the Friedmann
equation for the brane scale factor. We make a specific choice of $\hat T^5_5$
which is adjusted to stabilize the extra dimension. This makes it possible to
compactify the extra dimension with a single positive tension brane, and this
model provides a RS-type solution to the cosmological constant problem. When
the same idea is applied to the RS model with two branes, the wrong sign of
Friedmann equation for the negative tension brane can be resolved and usual FRW
cosmology is reproduced for the brane.
