It is thought 80 jobs will go this financial year and 211 before the end of the next at the Princess Royal Hospital and Royal Shrewsbury Hospital.
The Shrewsbury and Telford NHS Trust is in debt by £30m and a spokesman for Princess Royal Hospital said it needed to act or the debt would keep rising.
Last week it was announced that 1,000 jobs are to go at University Hospital of North Staffordshire.
A spokesman at the Princess Royal Hospital in Telford told the BBC it needed to be "more efficient".
"If we do not make the reductions that we need to make now it could be worse in the future"
"If we do not make the reductions that we need to make now it could be worse in the future.
"At the end of this year we will owe £31m and we cannot allow that to grow at £10m a year, we need to become more efficient."
The spokesman added the hospital hoped to make the cuts through natural wastage but compulsory redundancies had not been ruled out.
Mark Pritchard, the Conservative MP for Wrekin, is to meet union officials from Amicus, Unison and the Royal College of Nursing on Monday to discuss the cuts.
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