Visitors with cars displaying Edinburgh parking permits were spotted parking at beaches near Coldingham and St Abbs over the weekend.
Social distancing advice from the Scottish Government states that people should only travel for essential reasons such as buying groceries, healthcare, caring responsibilities or essential work.
And people should find ways to stay mentally and physically active by walking, running or cycling outdoors once a day for up to an hour close to home or by exercising indoors.
The RLNI have also issued warnings about surfing, swimming or sailing during the coronavirus.
Local MP, John Lamont, has contacted the police and the local council to ask that firmer action be taken against those who are breaking the rules.
He said: “It is very frustrating that people think they can come to the Borders to our beautiful beaches during this national crisis. The advice is clear – you should only travel for essential reasons and you should be exercising close to your home.
“Frankly, it is extremely selfish to travel from places such as Edinburgh and put local people at risk. The advice is there for a reason. Flouting the rules risks lives.
“Of course, if you live nearby it is perfectly acceptable to use the beach as part of your daily exercise.
“However, you must observe the social distancing rules and should not meet up with people outside of your own household.
“There will be plenty time to visit our stunning beaches and landscapes, as well as sample some of our local hospitality, when we have defeated this deadly disease.”
Councillor Carol Hamilton, who represents East Berwickshire, added: “At this present time, it is imperative for those people driving out of their locality to respect communities who are obeying the rules by staying at home and taking exercise locally.
“Day-trippers visiting during this crisis are causing distress and fear among the Berwickshire community.
“So I would ask visitors to stop, think twice before making that non-essential journey, wait until lockdown is over, and then come and visit the amazing Berwickshire coast and all it has to offer.”