Dorset County Hospital in Dorchester has declared a critical incident due to "extreme operational pressures" following the Christmas bank holidays.
The number of people being admitted to the hospital is exceeding the number of patients being discharged.
Staffing issues are also contributing to the problem.
By declaring a critical incident, the hospital is able to take extra steps to maintain safe services for patients.
In a statement the hospital said: "We are working with our system partners within the NHS and social care to see how they can assist us with patient flow and discharge."
The public is being asked to help the hospital in the following ways:
Only ever call 999 in the event of a serious or life-threatening emergency
Visit 111.nhs.uk or call 111 if you need urgent medical help and aren’t sure what to do
Being ready to collect your family or loved ones from hospital as soon as they are medically well-enough to leave
Do not come to our Emergency Department with minor injuries, as you will be signposted elsewhere. Minor Injuries Units are available to help with urgent care needs. Visit this website for more information on where they are and when to use them
Use your local pharmacy if you are able to as they can help with a range of minor health issues including colds, skin problems and earaches
Planned procedures and outpatient appointments are currently still going ahead but are under constant review.
The hospital is advising patients who have an appointment to attend as planned unless they are contacted directly.
The hospital says the situation with planned procedures and outpatient appointments is being monitored "very closely".
The hospital added: "As always, we remain committed to providing the best possible care for our patients and we thank you for your support and understanding at this challenging time."
Portsmouth Hospitals University NHS Trust has also declared a critical incident.
It is the second for the Trust in a matter of weeks, with a critical incident declared on December 20 which was stood down on December 23.
The Trust says the hospital and emergency department at the Queen Alexandra are full, with demand outstripping the capacity available in Portsmouth and South-East Hampshire.
A critical incident has also been declared by Surrey and Sussex Healthcare NHS Trust due to the significant ongoing pressure on local NHS services.
It says it's seeing record numbers of people attending A&E, calling NHS 111, accessing GP services and calling 999.