The paper considers the problem of packing a maximal number of identical circles of a given radius into a multiconnected domain. The domain is a circle with prohibited areas to be finite unions of circles of given radii. We construct a mathematical model of the problem and investigate its characteristics. The starting points are constructed in a random way or on the ground of the hexagonal lattice. To find the local maxima, a modification of the Zoutendijk method of feasible directions and a strategy of active inequalities are applied. We compare our results with the benchmark instances of packing circles into circular and annular containers. A number of numerical examples are given.