Jets emanating from AGN propagate first through an isothermal, but roughly power-law in density, galactic halo and then into a hotter, less dense, and uniform intergalactic medium (IGM) or intracluster medium (ICM). We use a three-dimensional boundary-following code (Mitteldorf & Wiita 1988), altered to allow for a two-phase external medium. We vary the beam power, P, the redshift, z, the radius of the galactic halo/IGM interface, Rh, the steepness of the power-law fall-off within the halo, n, and the temperature ratio of the IGM (or ICM) to the halo, Tr to estimate the average linear sizes of extragalactic radio galaxies (RGs). Good agreement is obtained with regard to the relationships between the overall linear size of such radio sources and both the total radio power (at fixed redshift) and the cosmological redshift (at fixed power). These numerical models tend to support recent analytical models (Gopal–Krishna & Wiita [GW] 1987, 1988).