A mathematical programming problem is proposed for form-finding of cable domes considering geometrical no linearity. The optimality conditions of the problem are derived to guarantee that the optimal solution coincides with the self-equilibrium configuration of the cable dome with specified member axial forces. The number of independent axial forces is investigated under the geometrical constraints as well as equilibrium conditions. An algorithm for design of cable domes is presented by using the primal-dual interior-point method. The self-equilibrium configurations are computed for cable domes to demonstrate efficiency of the proposed algorithm.