The son of a merchant, Sørensen studied law at the University of Copenhagen and at the Graduate Institute of International Studies in Geneva. He worked in the Danish Foreign Ministry from 1938. During his tenure there, he worked as Attaché Embassy in Bern and in 1944 as Secretary of Legation in London. In 1945 he was promoted to Deputy Head at the State Department. He left that post in 1947 to become a full professor of international law and constitutional law at the University of Aarhus. He obtained his doctorate in law.
Sørensen engaged in various positions of international politics and law. In 1949 he was a member of the Danish delegation to the London Conference on the Treaty of London, which established the Council of Europe. Between 1949 and 1951, he represented Denmark in the United Nations Commission on Human Rights. From 1954, he sat on the Sub-Commission on Prevention of Discrimination and Protection of Minorities for two years, and he also sat on a committee that deals with the application of the International Labour Organization addressed conventions until 1964.
In 1955 he was appointed to the European Commission on Human Rights where he sat until 1973. He served as president of that commission from 1967 to 1972. From 1956 to 1972, he also served as a legal adviser to the Danish Foreign Ministry. He headed the Danish delegation for the first and second United Nations Law of the Sea Conferences in 1958 and 1960, respectively. He was appointed to sit as judge ad hoc on the International Court of Justice by the governments of Denmark and The Netherlands for North Sea Continental Shelf cases (1968-1969). He retired from the University of Arhus in 1972.
From 1973 to 1979, Sørensen sat as a judge on the European Court of Justice. From 1980 to 1981, he sat as a judge of the European Court of Human Rights. He was the first of four lawyers who spoke at both institutions. He died in 1981 at the age of 68 years.
Sørensen was a member of the Permanent Court of Arbitration, the Institut de Droit International and sat on the boards of trustees of the Max Planck Institute for Comparative Public Law and International Law and the Hague Academy of International Law. At the latter he gave two guest lectures on "Le Conseil de l'Europe" (1952) and "Principes de droit international public" (1960).
Sørensen married Ellen Jacobsen, daughter of Major-General Carl Jacobsen in 1940.
Sørensen published his first legal paper at the age of 19, "La prescription en droit international". "Les sources du droit international" (1946) and his lecture "Principes de droit international public" at the Hague Academy of International Law (1960) are considered to be his most important works. He was editor of the international law textbook "Manual of Public International Law", which contained the contributions of lawyers from twelve countries. He belonged to the editorial board of the "Yearbook of the European Convention on Human Rights".
- Honorary doctorate from the Christian-Albrechts University of Kiel (1964)
- Honorary doctorate from the University of Strasbourg
- Manfred Lachs: The teacher in international law. 2. Auflage. Martinus Nijhoff Publishers 1987. S. 143–145.
- Yearbook of the European Convention on Human Rights. Volume 23, 1980, S. 50–53. Martinus Nijhoff Publishers.
- PDF of Chapter 8 - Presidents of the Commission, p. 125 of The Conscience of Europe - 50 years of the European Court of Human Rights, with all chapters available here.
- Erika Engel (u.a.): Europäische GRUNDRECHTE-Zeitschrift. Jahrgang 1980, S. 308. N.P. Engel Verlag, Kehl am Rhein.
- Internationales Biographisches Archiv 42/1981 vom 5. Oktober 1981
- Kurzbiographie auf der Webseite des EuGH
- Ignaz Seidl-Hohenveldern: Max Sørensen (19.2.1913 – 11.10.1981). In: Österreichische Zeitschrift für öffentliches Recht und Völkerrecht. Ausgabe 32, 129. Jahrgang 1982. S. 129.