A class of quasi-variational inequalities (QVI) of elliptic type is studied in reflexive Banach spaces. The concept of QVI was earlier introduced by A. Bensoussan and J.-L. Lions  and its general theory has been developed by many mathematicians, for instance, see [6, 7, 9, 13] and a monograph . In this paper we give a generalization of the existence theorem established in . In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators of monotone type (cf. ). We shall prove an abstract existence result for our class of QVI's, and moreover, give some applications to QVI's for elliptic partial differential operators.