The trust has explained the facilities have have been experiencing a prolonged and intense period of pressure, due to the exceptionally high levels of demand and the ongoing impacts from Covid.
Additionally, the trust said it is continuing to experience issues in discharging medically fit patients due to capacity issues within the local care sector.
Despite having declared a critical incident, the trust issued an assurance that urgent services, including cancer services and other time-critical procedures, will continue.
Patients will be contacted directly if they may be affected by delays to non-urgent treatment or postponed appointments.
The trust says anyone with an appointment in one of its hospitals who has not been contacted should continue to attend the appointment as normal.
Any postponed procedures or appointments will be rescheduled as soon as possible, its statement added.
Shrewsbury and Telford Hospitals apologised to everyone impacted by the decision.
The trust assured the public that despite the challenges faced, the hospitals remain fully open for anyone who needs medical help.