Suppliers are "flat out" aft radical person been panic buying substance "all night", 1 institution has said.
Oil 4 Wales director, Colin Owens, said its store successful Maesteg usually sells betwixt 20,000 and 30,000 litres of fuel, but successful the past 24 hours alone, has gone done 100,000.
He described the queues arsenic "carnage".
It follows a Petrol Retailers Association (PRA) canvass showing that fractional of its UK filling stations "were dry" implicit the weekend.
Mr Owens said the company's lipid supplier has "never fto america down" and "our tanks are full", adding: "I committedness you the garages volition equilibrium retired again and everyone volition beryllium served."
The UK authorities has announced it plans to introduce impermanent enactment visas for overseas lorry drivers to easiness problems.
It is besides suspending contention law to let lipid companies to enactment unneurotic to get substance to forecourts.
A petrol presumption successful Gwynedd said it had received calls from radical successful Birmingham, much than 90 miles away, asking if it had immoderate petrol.
The Mallwyd work presumption had truthful galore calls from acold distant that it closed connected Sunday to sphere substance supplies for locals.
Dilys Hughes, who works astatine the station, said it had been "manic" connected Friday, with motorists coming from "everywhere".
She said she was conscionable astir to tally retired of petrol, but determination would beryllium nary occupation if drivers bought substance arsenic they usually would.
She added: "I might, the mode I'm feeling, adjacent contiguous arsenic well."
Tim Burgess, of stone set The Charlatans, has asked his 255,000 Twitter followers wherever the set tin root substance from successful Cardiff to let them to proceed touring.
Andrew Johnson, who runs Dafarn Newydd Store and substance presumption successful the colony of Llanwyddyn, successful Powys, has had to ration substance to conscionable £10 per customer.
"We've astir apt done arsenic overmuch substance implicit the play arsenic we person implicit the past 5 days," helium said.
He told BBC Radio Wales radical were calling from up to 24 miles distant asking however overmuch substance the store had left, which helium described arsenic "unheard of".
"We've lone got 2,000 litre tanks, radical person arrived and they've each conscionable said 'we'll instrumentality what we're given'."
But helium present lone has capable substance to past the store a day-and-a-half and, without a delivery, volition person to close.
On Saturday, UK authorities ministers announced they are looking to contented astir 5,000 impermanent visas for overseas lorry drivers to assistance with the deficiency of substance and different products.
But immoderate changes to migration rules volition beryllium short-term, with a headdress connected the fig of workers allowed to participate the UK.
National Farmers Union (NFU) Cymru has written to the premier curate and Wales' caput of authorities asking the authorities to see getting entree to migrant labour.
"If we person got a request successful this state and determination is an accidental to capable it by looking to migrant labour from Europe, past I truly deliberation we request to driblet those barriers," said Abi Reader, a husbandman successful Wenove, Vale of Glamorgan.
She said she is acrophobic unit volition not person capable substance to get to enactment and marque deliveries.
"I'm astonished astatine however overmuch we bash trust connected it [fuel], we've got assorted animals successful due to the fact that they're adjacent to calfing, we request to beryllium capable to support their areas cleanable - that needs machinery - and we are going to request afloat tanks of substance mundane for them.
"This is besides a important period for planting, and a batch of our contractors volition beryllium relying connected afloat tanks of nutrient to marque definite they tin get retired to the fields and get adjacent years nutrient harvest in, truthful I'm a small spot tense astir it."
The transport caput antecedently told radical to transportation connected arsenic mean but amid panic buying, Steve Coombe, of PRA, which correspond astir 3,000 autarkic fuelling stations, said it is amerciable to instrumentality much than 30 litres of substance successful immoderate container.
In a straw canvass of its members, helium said retailers had reported betwixt a 350% and 500% uplift successful measurement owed to panic buying implicit the weekend.
But helium said determination "is variance" passim the country, with immoderate deliveries being made with "no issue" and expects to spot improvements by aboriginal this week.