A computational capability has been developed for predicting the entire flow field about bodies of revolution including the base region. The additional complexity of base bleed and base jet effects have also been incorporated into this new capability. The thin-layer form of the compressible Navier-Stokes equations is solved using a time dependent, implicit algorithm. Numerical solutions have been obtained for a secant-ogive-cylinder projectile for .9 M 1.2 both with and without base bleed. Base drag has been computed and compared with experimental and semi-empirical data. The reduction in base drag with base bleed has been clearly shown for various mass injection rates. Additionally, the effect of a centered propulsive jet on base flow has been computed where the free stream Mach number is 1.343 and the jet exit Mach number is 2.7. Computed results show both qualitative and quantitative features of the base region flow fields.