Christer Johansson, who witnessed the incident at the Slottsskogen park in Gothenburg, said the elephants appeared calm when they wandered away from the circus and grazed on the park's plants, The Local.se reported Wednesday.
"First, the staff of the circus had the elephants within the fences, but suddenly the gates were open and they walked out," he said. "Now they're free in the woods."
The Aftonbladet newspaper said the elephants were safely back within the circus' fence by late afternoon.
Jonas Wahlstrom of the Skansen Open Air museum in Stockholm said he suspects the incident was a publicity stunt.
"It's clear that this is a PR stunt. The elephants have certainly had a push in the backside as they escaped," he said. "Circus elephants are very tame and have been trained to do exactly what you want. If elephants panic, they can obviously run people down, but it would surprise me if this happened with circus elephants."