A number of garages throughout the county have had motorists forming long queues today.
Police have now warned they will take action if they think cars are posing a risk to public safety.
A spokesman said: “We are aware of drivers queuing at petrol stations across Sussex, which is causing disruption on a number of roads.
“Current government guidance is that the public should continue to buy fuel as normal and we would ask drivers not to join queues on forecourts and along the roads.
“Keeping our highways clear is essential for emergency service vehicles to respond to incidents swiftly and hindering them poses a serious public health risk.
“Please be aware of the wider safety implications of queuing around petrol stations and do continue to follow the latest government guidance around the buying of fuel.
“Our officers are working to ensure the roads remain safe for everybody and will take action against motorists considered to be posing a risk to public safety.”