Let Omega be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by H (a)(Omega) the Banach algebra of all bounded holomorphic functions on Omega, with pointwise operations and the supremum norm. We show that the topological stable rank of H (a)(Omega) is equal to 2. The proof is based on Suarez's theorem that the topological stable rank of H (a)(D) is equal to 2, where D is the unit disk. We also show that for circular domains symmetric to the real axis, the Bass and topological stable ranks of the real-symmetric algebra H (a"e) (a) (Omega) are 2.