(http://www.roman-empire.net/army/ilipa.html)
The Carthaginian commanders Hasdrubal and Mago led a force of 50'000 to 70'000 infantry and 4'000 cavalry,whilst Hannibal still loomed large in the south of Italy. Hasdrubal arranged the Libyan crack troops at the centre. The less well trained Spanish allies were stationed at the wings with war elephants in front of them. Meanwhile the cavalry was aligned behind those wings.
The Roman commander Scipio decided to ready his army early in the morning, assure that all had been well fed. Right from the beginning the Roman skirmishers (velites) and cavalry harrassed the Carthaginian positions. The weaker Spanish auxiliary forces formed the centre, the tough Roman legionaries stood at the sides. On Scipio's command the skirmishers and cavalry withdrew and drew up behind the legionaries on the flanks of the Roman force.
The Roman wings advanced quickly, at the same time performing a 90 degree turn toward the centre. While at the centre the Spanish auxiliaries advanced at a slower rate to avoid contact with the hardened Libyan forces in the Carthaginian centre.
As the two detached, fast-moving Roman wings closed on the opponent, they suddenly split. The legionaries swung back around to their original alignment and now drove into the elephants and the weaker Spanish troops behind them. The Roman skirmishers and cavalry combined into joint units and swung around 180 degrees to crash into the Carthaginian flanks.
Meanwhile in the Carthaginian side, the Libyan infantry in the centre could not turn and fight off the attack, as this would otherwise expose their own flank to the Spanish allies of the Romans looming in front of them. Also they had to contend with the out-of-control elephants which were driven towards the centre. A torrential rain came to the rescue of the Carthagians, forcing the Romans to retire. However, the Carthaginian losses have been very heavy. (http://www.roman-empire.net/army/ilipa.html)