Geometrical constraints are formulated as linear equations with respect to force densities and nodal coordinates. These constraints are incorporated into the adaptive force density method proposed by the authors for finding the non-degenerate and self-equilibrated configurations of tensegrity structures. The form-finding process is divided into two design stages: (1) finding the feasible force densities that satisfy the non-degeneracy condition, and (2) uniquely determining the configuration (nodal location) that satisfies the self-equilibrium conditions. The proposed method is demonstrated to be powerful for systematically searching new configurations of tensegrity structures subjected to given geometrical constraints.