Summary: A method is presented for numerically determining multivariable poles and zeros of nonspinning flexible space structures consisting of one rigid part and elastic appendages. Among many definitions of system zeros, transmission zeros are investigated relating the force/torque input applied at an arbitrary point and the translational/angular displacement output at another point. Computational algorithms are obtained for the cases when the modal data are given in terms of constrained modes and unconstrained modes. Investigations on duality and equivalency of these two approaches are made, and the relations of the numerical structures of the algorithms to controllability and observability conditions are also clarified. The proposed algorithms are demonstrated for a simple numerical model.