The Mid Yorkshire NHS Hospitals Trust is struggling to recruit enough doctors because of immigration rules.
Medics from outside the European Union are regularly employed to fill vacancies across the NHS, but Home Office regulations on visas are preventing some doctors from abroad coming to the UK to work.
The issue, which has been reported in other parts of the country, has led to treatment delays for patients, bosses have warned.
The trust, which runs Pinderfields, Pontefract and Dewsbury hospitals, is trying to fill hundreds of gaps in its staffing levels.
At a trust board meeting, interim director of workforce Angela Wilkinson said that recruitment of nurses had not been affected because they are a “protected” profession on the Home Office’s visa regulations.
But she said: “We are encountering significant problems with (recruiting) doctors.”
Medical director Karen Stone said: “We’ve had two particular cases, one of which involved a orthopaedic doctor.
“We applied for his visa month after month for six months and each time it was rejected, so there was nothing else we could do. That’s gone now.
“The nurses that are coming through the system aren’t affected because of the visa guidelines.”
A Home Office spokeswoman said last week that the current system was “in the national interest”.
It has also been revealed that the trust has 228 nursing vacancies, though just over 100 new contracts will be offered to graduates in September.
Director of nursing David Melia said that staffing levels during the winter months had remained more stable than in previous years.
He said: “We’ve seen a reduction in the number of vacancies this month.
“A new but pleasing trend is that this is the first year where from December to March we’ve not seen an increase in our nurse vacancies over that whole period.
“In previous years we’ve seen staff resign just before Christmas and then into the new year. But it’s been a steady ship this year.”