Michel Strauss studied with Paul Tortelier and Maurice Gendron at the Conservatoire in Paris, where he won first prizes for cello and chamber music, subsequently continuing his studies at Yale University with Aldo Parisot. In 1980 he became first cellist with the Philharmonic Orchestra of Radio France, and began teaching at the Paris Conservatoire in 1987. He also taught in The Netherlands, and was a jury member for a number of international music competitions. 

Strauss has worked with a number of important contemporary composers such as Maurice Béjart, Luciano Berio, Pierre Boulez, Henri Dutilleux, Philippe Hersant, and Krzysztof Penderecki. A number of their works are dedicated to him. He also collaborated in film music with Jean-Luc Godard and worked for the music theatre in Avignon.

As a chamber musician Strauss has worked with pianists such as Jean-Claude Pennetier, Georges Pludermacher and Henriette Puig-Roget, violinists Gérard Jarry, Tibor Varga and Sandor Vegh, and violists Gérard Caussé, Serge Collot and Bruno Pasquier, as well as with his former teacher cellist Aldo Parisot.