The 'Blues' have had problems with the behaviour of children at Stair Park in recent fixtures.
The club will issue two banning orders this week along with other criminal charges, according to the 'BBC'.
Stranraer have released a statement, pleading to the fans: "Some recent behaviour has been totally unacceptable.
"If you are a parent or guardian and your child attends the games, we need your support in having a word with them about their behaviour in and around the ground before they get dragged into something that can't be defended.
"We have many children/youths who attend games on their own, cause no issues at all and are very welcome.
"But, sadly, we have a minority who think it is acceptable to cause bother and it is these people we need to identify."