Health watchdog, the Care Quality Commission, has criticised 20 areas of care at hospitals in Hull, following inspections in February.
In his first report on the quality of services provided by Hull and East Yorkshire Hospitals NHS Trust, England's Chief Inspector of Hospitals rated both the Hull Royal Infirmary and Castle Hill Hospital at Cottingham as Requiring Improvement.
While end of life care, critical care and maternity and family planning services were rated Good - the inspection concluded that all other services were below required standards.
Inspectors found that both hospitals were facing staff shortages and insufficient capacity to deal with the increasing numbers of admissions.
Staffing levels and skill mix did not always meet national guidance, the report found, although the trust board had agreed to invest in recruiting more nurses, and was in the process of recruiting for doctors' posts.
At the Hull Royal Infirmary, the accident and emergency department was found not to have enough facilities or staff to deal with the numbers of patients attending. There was a lack of appropriate senior clinicians and the children's accident and emergency department could not provide a dedicated 24-hour service.
In response, the Trust says it was aware of some of the issues raised in the report, and is already actively making improvements.