Autofrettage is used to introduce advantageous residual stresses into cylinders. The Bauschinger effect can produce less compressive residual hoop stresses near the bore than are predicted “ideal” autofrettage solutions. A723 steel is used for compound cylinder. This paper extends the analysis to material the addition of pressure or of shrink-fitting to the cylinders, providing associated residual stress profiles following various amounts of further yielding due to a net external pressure. The Bauschinger effects for “realistic” – Bauschinger effect dependent autofrettage are obtained. The 2-D analysis is performed via the finite element method. The Bauschinger effect is found to significantly lower the beneficial stress due to autofrettage.