Telford's Princess Royal Hospital and Royal Shrewsbury Hospital have seen more than 130 people in its two emergency departments during peak times.
Simon Wright, chief executive of The Shrewsbury and Telford Hospital Trust (SaTH), said: “The demand currently facing our two hospitals and, indeed, the wider NHS locally and nationally, has been well reported on.
"We are currently seeing hundreds of people in our two emergency departments and a very high number of admissions, which means all of our ward areas are full.
The pressure on Shropshire's hospitals are reflected nationally as admissions rise.
Mr Wright praised staff at the two hospitals who, he said, were pulling together to care for patients amid very high demand across the NHS.
He said staff have been staying late to care for the sick and injured, catering staff have been making sure everyone is refreshed and people have been reporting for work even when not on duty.
Mr Wright said: “There has been incredible commitment from staff. We have seen colleagues voluntarily staying behind after their shift has ended to ensure that patients are being looked after with as much care and kindness as possible. We have had people coming into work when they are not on the rota to help with shortage on night shifts.
“That commitment to our patients does not just extend to our fantastic clinical staff. Our catering teams, for example, have been great in making sure the departments have refreshments when they might be finding it hard to get away for a drink.
“I also want to thank our patients, who have been incredibly understanding if they have had long waits in the hospital or if we have, unfortunately, had to postpone their elective operations. Where we have postponed procedures, staff have been reallocated to work in other areas, and I would like to say a big thank you to them for being so flexible with their working arrangements.”
Mr Wright also praised colleagues in the wider health and care system for their support.
He said: “Our local authority colleagues have been working really hard to help us to ensure we that patients with complex discharge needs are able to leave hospital. We have also had excellent support from our Clinical Commissioning Groups and other hospitals in the area, such as the Robert Jones and Agnes Hunt Orthopaedic Hospital in Oswestry and community hospitals, who have been ensuring that their beds are available and reaching into our hospitals to help out when and where they can.
“Although the current situation is very challenging for us, it also shows what incredible people work in our hospitals and in the NHS. I am very proud of our teams here at SaTH and want to publicly extend my heartfelt thanks to each and every one of them for their amazing care, kindness and dedication and such a difficult time.”