This paper proposed a new method, i.e., Z-plane, for the property identification of the position-singularity loci of the 6/6-SPS Stewart manipulators. After constructing the Jacobian matrix of the 6/6-SPS Stewart manipulator, a cubic polynomial expression in the mobile platform position parameters, which represents the constant-orientation position-singularity locus of the manipulator, is derived. Graphical representations of the position-singularity locus of the parallel manipulator for different orientations are illustrated with examples to demonstrate the theoretical results. In order to analyze the property of position-singularity loci of the 6/6-SPS Stewart manipulator in three-dimensional space, a novel method called Z-plane is proposed. Based on the above-mentioned analytical expression, a quadratic expression that represents the position-singularity locus of the manipulator in Z-plane is derived, and further the property of position-singularity loci of the manipulator in parallel Z-planes is identified in detailed. It is shown that position-singularity loci of 6/6-SPS Stewart manipulators in parallel Z-planes are all quadratic expressions including infinite hyperbolas, four pairs of intersecting lines and a parabola.