To undrape is to remove a drape or covering from something, revealing what lies beneath: She undraped the statue for the unveiling.
The word can suggest deliberate exposure, whether literal or figurative, and sometimes carries a hint of the theatrical or ceremonial.
1. undress — disrobe, Remove worn garments; unclothe (Remove one's garments); strip (Narrow elongated piece); divest (Rid of assets); doff · shed · peel · deshabille · bare · denude · expose · uncover · unveil · unswathe
2. reveal — unveil, Reveal something hidden; uncover (Reveal what's hidden); expose (Make known publicly); disclose (Reveal hidden information); unmask · uncloak · bare · show · display · manifest · unfurl · unfold · unroll · divulge