Caves of Ajanta (India). 'They may have been ascetics, but the 2nd-century-BC monks who created the Ajanta caves had an eye for the dramatic. The 30 rock-cut forest grottoes punctuate the side of a horseshoe-shaped cliff . The architecture and towering stupas made these caves inspiring places in which to meditate and live.' http://www.lonelyplanet.com/india/maharashtra/ajanta
The Catacombs in Alexandria are so called because the design was very similar to the Christian Catacombs in Rome. Most likely it was a private tomb, later converted to a public cemetery. It consists of 3 levels cut into the rock, a staircase, a rotunda, the triclinium or banquette hall, a vestibule, an antechamber and the burial chamber with three recesses in it; in each recess there is a sarcophagus. The Catacombs also contain a large number of Luculi or grooves cut in the rock.