Based on the general macroscopic potential theory, a method to find macroscopic plastic potential and the corresponding constitutive relation is developed for visco-plastic materials containing cylindrical voids. The constitutive relation of the matrix has a generalized overstress form. A comparison of the exact macroscopic potential with its upper bound is made. The numerical results show little difference between the upper bound potential and the exact one. The macroscopic constitutive relation is investigated under triaxial loading conditions. When the strain rate sensitive parameter tends to zero, Gurson's model (1977) is retrieved. When the loading condition is axisymmetric, the pres ent result reverts to Licht and Suquet's result (1988). When the matrix becomes infinite, the result of Budiansky et al. (1982) is obtained. Finally, the macroscopic constitutive rela tion and the corresponding dynamic loading surface are investigated for the case of axi symmetric load. An approximate analytical expression of the dynamic loading surface is suggested through analysis and numerical fitting.