We investigate constraints for including bulk and brane matter in the Randall- Sundrum model. In static configurations with two zero thickness branes, we find that no realistic brane matter is possible. We also consider the possibility that the radion has stabilized by dissipating its energy into the bulk in the form of some unspecified matter, and find the Randall-Sundrum cosmological solutions in the presence of bulk ideal fluid. We discover that the metric is necessarily in a static configuration. We also discover that there is only one allowed equation of state for the bulk fluid, $p= ho $, corresponding to the stiff ideal fluid. We find the corresponding brane cosmologies and compare them with the Friedmann-Robertson-Walker model.