In the last twenty years, the study of Noether's theory has become a popular topic by mechanicians, and a lot of remarkable generalizations have been made. However, all these researches were limited to systems with bilateral constraints, but, in practice, the problems with unilateral constraints are more interesting. In this paper, the Noether theorem and inverse Noether theorem for a dynamical system with unilateral constraints are obtained by using as main tool the notion of generalized quasi-symmetry (a special infinitesimal transformation of an \(r\)-parametric transformation group). Two examples illustrate the approach.