A boundary value problem for a periodic array of initially spherical voids in a power law creeping solid is analyzed. An axisymmetric cell model relevant for simulating grain boundary void growth is used. The rate boundary value problem is solved by means of a finite element method. Void growth histories accounting for void shape changes and, within the cell model context, void interaction effects are computed for various remote stress triaxiality states. An automatic remeshing algorithm permits computations for large changes in void size and shape. The computed void growth rates are compared with predictions from available analytical formulas that neglect shape change effects.