For the calculation of transonic laminar relative flow fields on the axisymmetric H-S and B-B stream surfaces in turbomachinery, a finite volume method developed in Part (I) is extended. Energy equation is replaced for simplicity by the condition of constant rothalpy throughout the flow fields. For axisymmetric H-S flow the circumferential componets of absolute velocity are given in advance so that this component of momentum equations can be neglected. Some numerical results show good agreement with experimental data.