The attack happened in the early hours of November 30 as the homeless men were sleeping in the doorway of a shop in Whitefriargate in Hull.
CCTV footage shows a man preparing for the assault by taking several strides backwards before running at the tent and jumping into it.
One of his friends appears to be recording the attack on his phone, and can be seen giggling as they make off.
A spokesperson for Humberside Police said the response to this appeal had been "overwhelming, with a number of leads now being followed up as the investigation continues".
Hull’s Neighbourhood Chief Inspector Michelle Garlick urged the men to hand themselves in.
She said: "After receiving the CCTV footage from Hull City Council, officers went out to locate the two victims, as the incident itself wasn’t reported to us and we wanted to ensure they had received medical attention if they were injured and to ensure their safety and welfare.
“Fortunately they were not injured, but as can be seen in the footage, they could very easily have been and with the force used, they could have suffered serious or life-threatening injuries.
“All of the police officers and PCSOs in Hull City Centre work closely with partners to support homeless people in the city.
"We have a daily contact with those who are sleeping rough and help to provide support and assistance wherever needed.
“The investigation is under way and I want to thank the public for their help.
"We have had numerous calls since the release was issued yesterday, with a number of leads we are currently following up and we are continuing to make enquiries.
“I would appeal for the men in the footage to please come forward and make contact with us, or for anyone who may have information on the incident, as these actions and behaviour will not be tolerated in our city.”
Anyone with information can call 101 quoting reference 16/124920/18.