Council leader Malcolm Pate and the authority's chief executive Clive Wright warned that without assistance they face a considerable reduction in the county's services.
They have urged either an increase in the amount they can raise in council tax or an alteration of the formula by which councils receive central Government funding.
The call came as the council's financial plans for 2016/17 were announced, which include about £30 million of cuts, and a proposal to raise council tax by four per cent.
The bleak financial situation could lead to as many as 150 services being affected, with leisure centres at risk along with maintenance of parks and local amenities.
Councillor Pate, who represents Albrighton, said: "One of the biggest problems is the move of resources from rural areas to urban areas. We are not alone in this. Our MPs are very supportive of that argument and they are proposing it down in Westminster.
"We are not asking for a bigger slice of more Government money but fairer distributions of the formula.
"We hope there may be some movement on that in the next few months."
Mr Wright said that the current funding system sees Shropshire disadvantaged against urban areas, while it also faces greater costs due to its ageing population.
He said: "The methodology for distributing funding is inherently unfair and disadvantages rural areas, particularly Shropshire. I would be happy if we could just have equal finding."
Councillor Pate said the authority's failure to increase council tax in the past six years was partly to blame for the situation – creating a £15 million gap in its finances.
He added: "Had they elected me in 2009 I do not think they would be in such a difficult position."