Thomas Brown, 17, was out with friends in Methil, Fife, on Friday when he became separated from the group at around 10pm and has not been seen since.
Police Scotland said it was very unusual for Thomas, who lives near Cupar, not to be in touch with his family.
They reported him missing at around 2pm on Saturday after becoming concerned that they had not received a telephone call or text.
Searches have been carried out by the police and relatives in the Steelworks Brae area where he was last seen and along the banks of the River Leven.
Divers are due to comb the river further this afternoon.
Inspector Andrew Sneddon from Police Scotland said: ''It is out of character for Thomas not to be in touch with his family and we are keen to hear from anyone who may have information as to his whereabouts.
''It may be the case that he has met other friends and does not realise we and his family are worried about him. We just want to be assured that he is safe and well.
''Additionally, the area in which he was last seen is well used by dog walkers and I would urge them to let us know if they see anything which may help us trace Thomas.''
The teenager is described as 5ft 5in, slim, with blue eyes and his hair is shaved at the sides but longer on the top. When last seen he was wearing a grey hooded top with a blue hood, a black Nike T-shirt with an orange logo and grey tracksuit trousers with denim pockets.
Anyone with information is asked to contact Police Scotland on 101 or Crimestoppers on 0800 555 111.