In 1996-1998 Bercovier set up the Computer Science department of a new university at Paris-La Defense (Pôle universitaire Léonard de Vinci).

He developed new Finite Element Methods for fluid flows and incompressible materials based on penalty and reduced integration methods that are universally implemented.Together with Pironneau, Olivier he proved the optimality of the Hood Taylor finite element for incompressible fluids.

[9] On the former subject, his book with Tanya Matskevitch is at the origin of numerous research on smooth surfaces over arbitrary quadrilateral meshes.

[citation needed] Parallel to his academic work, Bercovier has been involved in industrial research: he was Chief Consultant for Kleber and Michelin (1972 – 1985),[10] Hutchinson (1990-2017), Pechiney (1992-2017), L’Oréal (1996-2013).

Bercovier was also the chairman of Aleph Yissum[11] (now Ex Libris) in the years 1986 - 1996, and was active in turning the small start up into the leader in computer systems for libraries.

He was a member of the scientific council of AMIES, Agency for Interaction in Mathematics with Business and Society,[16] a founding member of the Israel Association for Computational Methods in Mechanics[17] and co-founder and chairman of the World User Association in CFD (Computational fluid dynamics).

His brother, Herve Bercovier, is a Professor (Emeritus) in the faculty of medicine at the Hebrew University of Jerusalem.

[23] Michel Bercovier is a co-founder and Honorary President of the Association du Festival Lyrique de Montperreux(fr).