Time-dependent numerical simulations of jets associated with compact steep spectrum (CSS) and possibly the gigahertz peaked spectrum (GPS) sources have been made. The goal is to determine if these objects can be permanently confined by a dense ISM in the core of an active galaxy. Propagation into both a homogeneous ISM with and without density gradients and a more realistic two-phase ISM populated with cold, dense clouds has been calculated. In general, CSS sources of low and intermediate luminosity can be confined by an ISM of average density 10 times that of the Galaxy