Between 5.30pm and 6.30pm - potentially seven hours later - the woman and child were forced out of the vehicle on Kirkleatham Lane, between the turn off for Kirkleatham Museum and the bus stop towards Redcar.
They ran across the road and towards the wooded area.
The first suspect, who was driving the vehicle, is described as a white male, aged in his late twenties or early thirties, around 5ft 7' to 5ft 10' tall.
He is of large build, with short, brown hair and has the word 'love' tattooed across his knuckles.
The second suspect, a passenger in the car, is described as a white male, aged in his early twenties.
He is around 5ft 5' to 5ft 6' tall, of medium build, clean shaven and with brown hair and had a local accent.
Temporary Detective Chief Inspector Matt Murphy-King, of Cleveland Police, said: "This has been a very traumatic ordeal for the victim and her child.
*** Detectives Appeal for Information Following Rape, Redcar ***
Police are continuing to investigate the rape of a...
Posted by Cleveland Police on Sunday, 5 March 2017
"Thankfully, incidents of this nature are rare and this is an isolated incident.
"There are a team of detectives working on this investigation and we have increased patrols in the local area.
"Redcar sea front is a busy area and, as a precaution, I would encourage anyone in the local area to be extra vigilant.:
Detectives are appealing to anyone who may have seen two men in a dark saloon in the area around the time of the incident on the sea front on Friday or anyone who may have seen the men or the vehicle in Yearby the same day to get in touch.
They are also appealing to any witnesses who may have seen a woman and child in a distressed state in the area of Kirkleatham Lane on Friday evening.
