Whitehaven supermarkets are running low on some items meaning they have had to limit some items.
Toilet rolls, pasta, rice, hand wash and tinned tomatoes are all items which are running low. Some other foods are also in short supply.
Signs are now also on display limiting some items to 5 per customer in Tesco.
In Tesco shoppers are limited to buying no more than five of certain goods, including antibacterial gels, wipes and sprays, dry pasta, UHT milk and some tinned vegetables.
The rules apply in stores and online.
A government spokesperson said it was in touch with UK supermarkets to "discuss their response" to the virus.
