The charging curves and the saturation values of both charge and potential have been determined for six metal models with typical ice crystal shapes (bullet, columns, needle, plate, and dendrite) with different orientations in a unipolar ion current, in conditions that make the charging process field controlled. Metal spheres of several sizes were also used, as a reference. It was found that the theory of field-controlled charging for spheres adequately describes the process for ice shapes, provided the variable (charge or potential) is multiplied by a factor depending on shape and orientation. Thus the saturation charge per unit cross section exposed to the ion current varied from 0.4 to 15 times that for a sphere, for the models used. The results are relevant to the formation of shielding layers at the upper level of thunderclouds. The measurements also provide estimates of a parameter (numerically equal to capacitance) that controls the rate of growth by sublimation.