Yes, people with a diagnosis of high blood pressure (hypertension) routinely have surgical procedures performed, including surgery that requires general anesthesia. Before elective surgery is performed, the surgeon or primary care physician will review your medical history and perform a physical examination. If your blood pressure is too high to safely proceed, then your doctor will advise an adjustment in medication.
If the surgery is not needed urgently and your blood pressure is not controlled, then the date may be rescheduled to allow time for the blood pressure to slowly come down and stabilize. Just quickly reducing blood pressure, without letting your system adjust -- especially the kidneys -- can lead to complications.
