It has an area of 65.80 km2 and stands at an elevation of 2260 metres above sea level.
Its name, Atzompa, comes from the nahuatl language and refers to the small river valleys on the mountain looking like a scalp[1] In time it took the other part of its name from the Soledad river which runs through the town.
The municipality of Soledad Atzompa is delimited to the north by Huiloapan de Cuauhtémoc, to the east by Atlahuilco, to the southeast by Xoxocotla, and to the west and northwest by Acultzingo.
[2] There had been a number of border disputes in the past settled by a decree in 1982.
[1] The local soil is composed of sandy rock and only 50% can be used for agriculture.