This chapter is devoted to Louis Poinsot’s criticisms toward Lagrange’s Méchanique analitique of 1788, assuming a reductionist approach. The first part introduces Poinsot’s mechanics which also takes account of the existence of constraints. Poinsot believes that VWLs have no interest for mechanics. The final part of the chapter is a report on the demonstration of a law of virtual work similar to that of Lagrange in which use is made of velocities and not infinitesimal displacements. Although Poinsot considers this demonstration only a trivial corollary of his mechanics, it had a remarkable success.