Abstract: Schwartz-MacPherson classes were defined in 1965 by Marie-Hélène Schwartz, in the framework of obstruction theory, using “radial” vector fields and Whitney stratifications, then by Robert MacPherson, answering a conjecture by Deligne and Grothendieck. Although Schwartz’s definition is easy to understand, using Whitney stratifications requires delicate and very technical constructions. The use of Lipschitz stratifications makes it possible to simplify the construction of the radial vector fields and therefore the construction of classes, remaining within the framework of obstruction theory. This is a joint work with Tadeusz Mostowski and Nguyen Thi Bich Thuy.