The mode analysis of an open-boundary Cerenkov laser is developed in the collective regime. The Cerenkov laser under consideration is composed of a magnetically-confined relativistic electron beam and a dielectric-loaded conducting plane. The electron beam and the dielectric are assumed to be arbitrary in thickness, with an arbitrary spacing allowed between them. For the Cerenkov laser specified above, the following results are obtained. First, an electromagnetic wave mode is coupled with an infinite number of space charge wave modes. In the general case, an electromagnetic wave mode is coupled collectively with space charge wave modes. On the other hand, in the special case where the coupling occurs near the Cerenkov threshold, an electromagnetic wave mode is coupled separately with each of space change wave modes. Second, the characteristics of the growing wave for a magnetically-confined beam are similar to those for an ion-neutralized beam, except that the magnitude of the spatial growth rate becomes somewhat smaller for the former than for the latter.