Hywel Dda Health Board has cancelled elective or planned surgery under pressure from a large increase in the number of emergency patients requiring hospital admission.
Hospitals in Carmarthenshire, Ceredigion and Pembrokeshire have all reported "extreme pressure" common across the NHS during winter months, a spokesman said.
"These very sick patients must be our priority and so the decision has been made with careful consideration to reschedule some elective (planned) surgeries at Bronglais, Glangwili, Prince Philip and Withybush Hospitals from Tuesday, January 8.
"Affected patients will be contacted at the earliest opportunity and every effort will be made to rebook their surgery as soon as possible.
"All cancer related or urgent cases will not be affected and emergency surgery will continue," she added.