Shrewsbury & Telford Hospital NHS Trust (SaTH), which runs Royal Shrewsbury Hospital (RSH) and Princess Royal Hospital in Telford, said it had been "experiencing high levels of demand in recent days".
It comes after footage shared on social media shows as many as 14 ambulances waiting outside RSH believed to be on Thursday.
A spokesman for SaTH said: “Our accident & emergency departments have been experiencing high levels of demand in recent days and we are continuing to work hard to ensure that everyone receives the quality care they need.
“We also continue to urge everyone to consider whether they need to attend A&E – which is for genuinely life-threatening emergencies – or whether another part of the healthcare system would be better placed to provide the type of care they need.
"GPs’ surgeries are open, the 111 service is available to help if you have an urgent medical problem and aren’t sure what to do, pharmacies – which are staffed by trained medical professionals – can assist with a wide range of issues, and urgent treatment or minor injury centres are available across the county.”