Haptic perception of volume (Experiment 1) and surface area (Experiment 2) was studied with tetrahedrons, cubes, and spheres as stimuli (2–14 cm3). The results of Experiment 1 showed that subjects perceived a tetrahedron to be larger in volume than either a cube or a sphere of the same physical volume and that they perceived a cube to be larger than a sphere. This pattern was independent of object size. The biases were smaller in conditions with mass information than in those without. The average biases in the different conditions ranged from 7% to 67%. Analyses revealed that the subjects apparently based their volume judgments on the surface area of objects. Experiment 2 showed that surface area itself could be perceived accurately, almost independently of the objects’ shape. Experiment 3 investigated volume perception of objects in the absence of surface area (wire-frame objects) and showed larger biases than those observed with solid objects. With wire-frame objects, the maximal distance between two vertex points was probably the dimension on which the volume judgment was based. In conclusion, haptic volume perception of geometric objects has to be inferred from other object properties, but surface area can be perceived unbiased.