Nigel Lee, Chief Operating Officer at The Shrewsbury and Telford Hospital NHS Trust (SaTH), said the situation had resulted in longer waits for people attending A&Es at both Princess Royal Hospital in Telford and Royal Shrewsbury Hospital.
One of the delays in providing treatment is created by the systems set up to minimise the risk of people spreading coronavirus.
He said that new facilities are being set up at the hospitals in an effort to reduce the strain on the A&E departments.
He said: “Like many hospitals, we experience a high number of people coming to our emergency departments and I would like to apologise to any patients who have faced a longer wait for treatment.
"Patients are assessed on arrival at A&E and prioritised in accordance with their clinical need. With Covid-19 in our community, patients arriving at both A&Es are further categorised and segregated relating to symptoms and Covid-19 related risk.
"Due to the large numbers of people seeking emergency care, we are sorry that this means some patients waiting longer than they should in our A&Es but it is vital that clinical safety is our priority."
Mr Lee said that the number of people attending the hospitals – particularly with more serious problems – was increasing to the levels seen before the pandemic.
He said: “We are seeing an increase in patients presenting with complex conditions and levels of ‘majors’ patients are at pre-Covid-19 levels.
"We are working closely with our local system partners, both in the NHS and in social care, to best cope with the demand we are seeing.
“Going forward, to ensure patients are seen and treated as quickly as possible we are creating a new Same Day Emergency Care Centre at the Royal Shrewsbury Hospital and a 17-bed Unit at the Princess Royal Hospital in Telford.
"Both will help to ease pressures on our A&E and improve care for our patients. These will be available after Christmas."
Mr Lee also urged the public to make sure they get the flu jab if they are eligible, and to use NHS 111 for medical help.
He said: “The public can help NHS staff by getting their flu jab if they’re eligible, talking to a pharmacist for expert advice about winter bugs before they get worse, or using the NHS 111 phone or online service if they need medical help fast but aren’t sure what to do.”