Posted on a website by Islamic State, the images appear to show the statues being brought into a public place and then attacked by militants with large hammers.
The accompanying text describes how the statues were found in the possession of a lone smuggler in Aleppo province in the north of Syria.
According the posting, an Islamic State court in Manbij (the administrative centre of the area controlled by the militant group) sentenced him to a public beating (apparently pictured in the image below), and ordered the destruction of the ancient artefacts.
The international community has been waiting for news of the fate of the priceless historic site of Palmyra ever since it was taken by IS in late May.
Palmyra contains some of the world’s best preserved Roman ruins, and there have been reports that since taking over the jihadist group has planted mines and bombs in the area.
On 23 June IS said it had blown up two shrines at the Palmyra site, among them to be the tomb of Sheikh Mohammed Ali, because it believed it to be sacrilegeous.