Members of the Independent Workers of Great Britain voted to continue a boycott of outlets in the city between 5pm and 10pm every night.
In a video message, one member says strikes are also taking place in Chesterfield, Sunderland and Blackpool.
He added: “We are going to take over the UK and leave Stuart Delivery no choice but to pay us better - and we are going to win this!”
The drivers are employed by Stuart Delivery which is sub-contracted by Just Eat.
WHAT IS THE STRIKE ABOUT?
They are protesting over a wage cut on December 6 which saw the minimum fee for journeys below half-a-mile drop from £4.50 to £3.40.
They say the leaves them on less than the National Minimum Wage after paying for car insurance, petrol and other costs. And they are calling for a minimum of £6 plus mileage per delivery, £15 per hour for waiting times after 10 minutes and a recruitment freeze.
But Stuart Delivery says fewer four per cent of deliveries are less than half-a-mile and under the new system ‘a substantial proportion’ will be paid more.
In a post on Twitter, ‘IWGB Couriers Sheffield’ state: “Strike week two and we are stronger than ever! Sheffield delivery drivers are united, focused & not backing down. Stuart Delivery and Just Eat listen to your workers and implement a pay rise now so we can return to serving our communities.”
WHY IS SHEFFIELD TUC BACKING THE DRIVERS?
Sheffield Trade Union Council is backing the strike.
Martin Mayer, Sheffield TUC secretary, said: “These are some of the lowest paid and most exploited workers in our city. They deserve a pay rise, not a pay cut!
“They are also demanding official recognition of their union and resolution of a number of grievances including unfair sackings for no reason and with no right of appeal.”
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He added: “Stuart Delivery are the villains of the piece here as they are the ones who have imposed the pay cut.
“But they are subcontracted by Just Eat, so Just Eat has to take full responsibility for the way these IWGB members are being treated.”