The two haulage firms, Hoyer UK and Suckling Transport, say unions rejected a pay offer which would take the drivers' average salary to £41,500 by January 2009.
"We wanted to resume further talks and are extremely disappointed the union plans to strike again so quickly," said Bernie Holloway from Hoyer UK, which is contracted by Shell to deliver fuel.
A Unite spokesman earlier said the company's offer would have increased salaries from just under £32,000 to £36,000. He said the companies' £41,500 figure could only be reached if possible overtime was included.
Unions point to Shell's bumper profits - helped by rising oil prices - and say drivers earn the same as they did in 1992 when they were directly employed by Shell.
Shell UK boss James Smith on the strike
Since then, Shell has outsourced the tanker driving jobs, handing the contract to an external company.
As a result, Shell said that it has no role to play in the current dispute as the pay row was between two of its suppliers and their workers, and does not involve Shell staff. It said it would not intervene in the dispute.
Union officials warned that the "dispute will carry on until Shell comes to the table".
"Driving a fuel tanker is a skilled and dangerous job," said Tony Woodley, joint general secretary of Unite, who joined the picket line at Stanlow, Ellesmere Port.
"The drivers are on £31,800. That is not a great deal of money. If they had remained with Shell, workers would be on £46,000."
Union members have set up picket lines outside Shell sites at some oil terminals around the UK. About three quarters of all fuel depots are not affected by the strike.
The scene at Kingsbury oil depot
At Shell's refinery in Stanlow, drivers held pickets, which read "Shell profits gush" and "Drivers' pay trickles".
Some tanker drivers not employed by the two firms are also refusing to cross picket lines.
Hoyer UK's Mr Holloway said most of its drivers who were not on a Shell contract were working normally.
The UK Petrol Industry Association (UKPIA), which represents oil refiners, said that stocks at forecourts were at normal levels and most garages would have around four days of supplies.
UKPIA estimated that demand for fuel was 30% higher than average for the time of year but said the industry could cope with the strike.
The Petrol Retailers' Association (PRA) said there were "significant sales increases" in some areas, with sales up 15% to 20%.
Overall stations are "well placed" for stocks, though some Shell stations said they would "have critical stock positions during the weekend", the PRA said.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.