Abstract: Issues of boundary discretization of the boundary element algorithm and effective measures to enhance the computational accuracy and numerical stability are investigated for the extraction of capacitance matrices of complex microfine wires. The influences of open boundary size, open boundary discretization, conductor discretization on the computational accuracy, as well as the issues of pseudo-solutions and matrix singularity are analyzed. A two-stage automatic iterative boundary element algorithm (AITEBEM) based on the conductor discretization iteration and the open boundary iteration is proposed. The detailed treatment of boundary discretization for the multilayer dielectric problem of wires with insulating covers and the semi-open space problem containing an infinite ground plane are described. The proposed algorithm has the advantages of low computational cost, high computational accuracy and numerical stability, as verified by three examples. The calculated results are well in agreement with those of the finite element method and the semi-analytical method.