Walsall Healthcare NHS Trust bosses said the number of patients being admitted was on the rise while the number of hospital staff being off ill was higher than the the first wave.
As a result, some of the non-urgent work usually carried out by the hospital is being put back as doctors and nurses cope with Covid and other emergency admissions.
But the trust also moved to assure residents that the hospital was very much "open for business" to anyone who was ill and measures were being put in place to ensure safety.
At a local outbreak engagement board meeting on Monday , the trust’s Matthew Lewis said: "We’re seeing rising numbers in the hospital, approaching the levels we experienced during the first outbreak and we’re having to take measures to manage this extra capacity.
“We’re having to reduce some of our routine work in other areas in order to allow us to look after patients in these areas.
"And we’re having to remodel our staffing plans so that we can make sure that we’re managing the patients that come in as safely as we possibly can do.
"It is putting a significant strain on us and we’re not able to do the routine work that we would normally do and we would very much encourage people in Walsall to follow the guidelines.
"The rules are there to help protect people in Walsall and to make sure the hospital can cope with sick patients when they attend.
"Some routine planned work will not take place at the moment so we can make sure we prioritise patients who are coming in urgently."
He added: "We are very much open to see patients who are sick with Covid and we are very much open to see patients who are sick with any other condition as well.
"We will take measures within the hospital to separate patients who don’t have Covid from those who do to make sure we protect and treat all patients and we don’t expose those who don’t have Covid to unnecessary risk."
His colleague Darren Fradgley added: "Our staff are not immune from the virus and we are seeing higher sickness rates and higher illness rates in wave two than in wave one.
"That is putting a pressure on all of the services we are providing, which makes the job even harder."
"Secondly, from a public confidence perspective, we are absolutely here to look after people in their hour of need and we’ll continue to do so.
"But we need the public to really respect and follow the rules so that we can do our jobs safely with the lowest possible transmission rates because the more staff we lose through cross infection, the less care we can provide to the community."
Dr Anand Rischie, chairman of the Walsall clinical commissioning group, said essential primary care services were also still available.
But he added doctors were working differently to reduce the risk of transmission via telephone calls and online advice and support.