The government is due to reveal how much money it will give to councils in England to help provide services.
Ministers are ready to use capping to keep council tax bills down
The settlement, which overall provides an increase in real terms of just 1% next year, has been described by councils as particularly tough.
Council chiefs say local authorities will face "tough choices" between cutting services or council tax rises.
But ministers claim the deal is "fair and affordable" and there will be "no excuse" for big tax hikes.
The settlement will be the first time every council has been told its grant allocation for each of the next three years.
BBC local government correspondent John Andrew said the expected 1% increase next year will be followed by two even leaner years.
Councils say the news comes when the cost of many services is rising well above inflation.
Our correspondent said the biggest pressures were in social services - with councils increasingly rationing care for the elderly so that only those whose needs are substantial or critical will get help.
The cost of waste disposal is also increasing, with landfill tax due to rise sharply in the next three years.
The Local Government Association (LGA), which represents councils in England and Wales, says extra pressure from immigration, free bus travel and an ageing population meant it was facing "the worst settlement for a decade" from government.
Its chairman, Sir Simon Milton, said: "Many council leaders will be scratching their heads as they try to work out how they will deliver ever-better services for local people with less money than in recent years and with greater demands on services."
The LGA says councils are £250m short of the money needed to deal with the impact of immigration because of inaccurate population statistics.
But Local Government Minister John Healey will say there is "no excuse for excessive council tax rises or any reduction in the quality of services" because the settlement is fair and extra pressures, such as immigration, have been taken into account.
Ministers are ready to use capping to keep council tax bill rises substantially below 5%, but they will not say whether that means bills going up by less than this year's average of just over 4%.