The cancellations affect admissions for Friday and Monday.
Oxford University Hospital's chief nurse Catherine Stoddart said it was so "patients with the most urgent needs can be treated more quickly".
Patients have been notified of the decision and urgent admissions will go ahead as planned.
Ms Stoddart said: "We have taken this decision to improve the flow of patients through the hospital so we can ensure that we can continue to see patients in our Emergency Department in a timely way."
She said because of increased demand "we would like to remind people across Oxfordshire to stop and consider all the options available to them before deciding to go to an Emergency Department".
She added: "Oxford University Hospitals' performance is in line with most other trusts in the current climate.
"We are continuing to work hard with colleagues in social care and our own supported discharge services to discharge patients who no longer need our care in order that patients who do need to be admitted can be seen within the appropriate timescales."
The hospital is currently at Escalation Level 3, which means there are "major pressures compromising patient flow" and "further urgent actions are now required".
Data leaked to the BBC earlier this week suggested 66 out of 152 hospital trusts raised the alarm as mounting bed shortages led to large numbers of patients experiencing trolley waits and delays in A&E in the first week of the year.
Over four in 10 hospitals in England declared a major alert as they encountered unprecedented pressures.
The John Radcliffe Hospital has cancelled all non-urgent operations because of "significant pressures" on its emergency department.