In three experiments participants haptically discriminated object shape using unimanual (single hand explored two objects) and bimanual exploration (both hands were used, but each hand, left or right, explored a separate object). Such haptic exploration (one versus two hands) requires somatosensory processing in either only one or both cerebral hemispheres; previous studies related to the perception of shape/curvature found superior performance for unimanual exploration, indicating that shape comparison is more effective when only one hemisphere is utilized. The current results, obtained for naturally shaped solid objects (bell peppers, Capsicum annuum) and simple cylindrical surfaces demonstrate otherwise: bimanual haptic exploration can be as effective as unimanual exploration, showing that there is no necessary reduction in ability when haptic shape comparison requires interhemispheric communication. We found that while successive bimanual exploration produced high shape discriminability, the participants’ bimanual performance deteriorated for simultaneous shape comparisons. This outcome suggests that either interhemispheric interference or the need to attend to multiple objects simultaneously reduces shape discrimination ability. The current results also reveal a significant effect of age: older adults’ shape discrimination abilities are moderately reduced relative to younger adults, regardless of how objects are manipulated (left hand only, right hand only, or bimanual exploration).