One of the many sieges where the Romans used the Ballista was the Siege of Aracillum in 25BC. The siege was fought during the Cantabrian Wars between the Romans and Cantabri. The Roman Generals in charge were Gaius Antistius and Augustus Caesar, they commanded five roman legions which consisted of about 6,000 men each and made up a total of 30,000 men. The Cantarbri forces stationed at Aracillum had about 15,000 to 25,000 men. They were positioned on a hill and had fortified the area. They used wood and sharpened stakes protect themselves from archers, ballista and cavalry.

The Roman forces had complete surrounded the hill fort and had built a wall around the fort which spaned over 20 kilometres and prevented the defenders form getting supplies or reinforcements. After several weeks the Cantarbri forces were starving and most committed suicide instead of getting captured and turned into slaves by the romans.

Eventually all the Cantarbri were killed by either the Ballista which were bombarding the fort or by starvation, those who survived the siege were taken prisoner and turned into slave.

The site of the siege is located in present day Spain, but the exact location still remains a mystery due to there being no remains to the fort or siege.

The ballista which were used in this siege played a crucial role. They spent the siege bombarding the enemy fort and managed to cause lots of damage to the defenders and the forts walls.

 

References:

https://www.revolvy.com/topic/Siege%20of%20Aracillum%20(25%20BC)&item_type=topic

https://en.wikipedia.org/wiki/Siege_of_Aracillum

http://www.wow.com/wiki/Siege_of_Aracillum