Void growth in an anisotropic ductile solid is studied by numerical analyses for three dimensional unit cells initially containing a void. The effect of plastic anisotropy on void growth is the main focus, but the studies include effects of different void shapes, including oblate, prolate or general ellipsoidal voids. Also other 3D effects such as those of different spacings of voids in different material directions, and effects of different macroscopic principal stresses in three directions are accounted for. It is found that the presence of plastic anisotropy amplifies the differences between predictions obtained for different initial void shapes. Also, differences between principal transverse stresses show a strong interaction with the plastic anisotropy, such that the responseis very different for different anisotropies. The studies are carried out for one particular choice of void volume fraction and stress triaxiality.