In five experiments, we tested the accuracy and sensitivity of the haptic system in detecting bilateral symmetry of raised-line shapes (Experiments 1 and 2) and unfamiliar 3-D objects (Experiments 3-5) under different time constraints and different modes of exploration. Touch was moderately accurate for detecting this property in raised displays. Experiment 1 showed that asymmetric judgments were systematically more accurate than were symmetric judgements with scanning by one finger. Experiments 2 confirmed the results of Experiment 1 but also showed that bimanual exploration facilitated processing of symmetric shapes without improving asymmetric detections. Bimanual exploration of 3-D objects was very accurate and significantly facilitated processing of symmetric objects under different time constraints (Experiment 3). Unimanual exploration did not differ from bimanual exploration (Experiment 4), but restricting hand movements to one enclosure reduced performance significantly (Experiment 5). Spatial reference information, signal detection measures, and hand movements in processing bilateral symmetry by touch are discussed.