June 4 – After arriving at Canada, the Royal Navy fleet sails out of British-controlled Halifax toward the St. Lawrence River to prepare the invasion of French Quebec. 
June 15 – The first vascular surgery in history is performed by a Dr. Hallowell (whose first name has been lost to history) at Newcastle upon Tyne, who uses suture repair rather than a tying off with a ligature to repair an aneurysm on a patient's brachial artery. The case is reported in 1761 by Dr. Richard Lambert in the paper "A new technique of treating an aneurysm", published in the journal Medical Observations and Inquiries.  The new procedure of reconstructing a damaged artery replaces the practice of ligation that had risked the amputation of a limb or organ failure. 
June 26 – After the fleet finishes navigation of the St. Lawrence and arriving Île d'Orléans, British troops go ashore at France's North American territory and begin the siege of Quebec City
Madame du Coudray publishes Abrégé de l'art des accouchements (The Art of Obstetrics), and the French government authorizes her to carry her instruction "throughout the realm" and promises financial support.