Police were called to Wellhead Park in South Street, Bourne at 10am on Friday and arrested a group of men who were acting drunkenly. There were also reports that one had exposed himself and the group had been swimming in the river.
The group may also have been involved in an incident at 9am on the same day, where a number of men were seen exposing themselves outside Bourne Grammar School.
One of the group, a 23-year-old man from Peterborough was given an £80 fine. The three other men were released without charge.
Insp Gary Stewart said that drunken behaviour would not be tolerated.
He said: "Behaviour such as this will not be tolerated, as it can be extremely offensive and alarming to the community.
"I would like to send out a strong message to people to think twice before embarking on this type of activity. What may start out as drunken antics can quickly escalate into criminal behaviour, and lead to arrest and prosecution.
"The public has a right to expect a certain level of decent behaviour when they are out and about, and anyone who is unwilling to adhere to this will be dealt with appropriately."
Insp Stewart also warned against the dangers of swimming in rivers and waterways.
He said: "Please don't be tempted, despite the nice weather to swim in these places. It can be extremely dangerous, both for you and for anyone who attempts to rescue you and could end in tragedy."