Geological objects that do not deform homogeneously with their matrix can be considered as inclusions with viscosity contrast. Such inclusions are generally treated as initially spherical or ellipsoidal. Theory shows that ellipsoidal inclusions deform homogeneously, so they maintain an ellipsoidal shape, regardless of the viscosity difference. However, non-ellipsoidal inclusions deform inhomogeneously, so will become irregular in shape. Geological objects such as porphyroblasts, porphyroclasts and sedimentary clasts are likely to be of this kind, with initially rectilinear, prismatic or superelliptical section shapes. We present two-dimensional finite-element models of deformed square inclusions, in pure shear (parallel or diagonal to the square), as a preliminary investigation of the deformation of non-ellipsoidal inclusions with viscosity contrast. Competent inclusions develop marked barrel shapes with horn-like corners, as described for natural ductile boudins, or slightly wavy rhombs. Incompetent inclusions develop 'dumb-bell' or bone shapes, with a surprising degree of bulging of the shortened edges, or rhomb to sheath shapes. The results lead to speculation for inclusions in the circle to square shape range, and for asymmetric orientations. Anticipated shapes range from asymmetric barrels, lemons or flags for competent inclusions, to ribbon or fish shapes for incompetent inclusions. We conclude that shapes of inclusions and clasts provide an important new type of strain marker and competence criterion. Copyright © 1996 Elsevier Science Ltd.