Patients are being advised to avoid accident and emergency departments unless their condition or injury is life-threatening.
Hospitals are facing "extreme pressure" over the new year period, officials at NHS Shropshire, Telford and Wrekin have said.
Rising flu and Covid-19 numbers, as well as workforce sickness, has led to a strain on services, it added.
Earlier in December, the trust declared a critical incident due to high demand.
Patients with non-urgent symptoms may face a long wait to be seen as those with the highest level of need will be prioritised, the NHS group said and urged people to ring 111 instead.
Some routine operations are likely to be rescheduled, it added, but cancer and other critical operations will continue to be prioritised.
"I am urging everyone in the county to only come to A&E for life threatening conditions and injuries. Please do not to call 999 or attend A&E unless it's a genuine emergency," said Alison Bussey, chief nursing officer for NHS Shropshire, Telford and Wrekin.
"Despite the severe challenges faced, our services remain open to anyone who needs them during this very busy period."
Minor Injury Units are located in Bridgnorth, Ludlow, Oswestry and Whitchurch and can provide advice and treatment for a range of minor injuries.
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Avoid accident and emergency, Shropshire patients advised – BBC
