Police were called by Solent Coastguard at 1:21pm on Monday after the pair was last seen near Appley Tower at around 12 noon.
Officers are helping the coastguard with an ongoing search of the area.
According to the Maritime Coastguard Agency, one of the boys is 6 years old and is wearing pale blue trunks, with dark brown hair, pale skin and dark brown eyes. The missing 8 year old is wearing red trunks and has a mole on his left shoulder.
The MCA appealed to anyone who sees the missing children to call 999 and notify police.
UPDATE 1500: Coastguards have appealed for the parents of the missing children to get back in touch with the police on 999.
Listen to Maggie Hill from the Maritime and Coastguard Agency by clicking the above link.
UPDATE 16:21 Coastguads said "We've searched the sea and shore and we now don't think there are 2 kids in danger. Search stood down. Thanks to everyone for their help."