Models play important roles in the design, simulation and measurement of touch probes. Although existing pre-measuring and empirical models can ensure measuring accuracy and resolution, they are independent of each other. Additionally, pre-measuring models have complex expressions with limited assumptions, while empirical ones ignore the probe’s working process. In this paper, a flexible-hinge touch probe with a decoupled Hexflex structure is proposed, and a corresponding three-dimensional (3D) parametric model is established by force-displacement analysis. The decoupled model exhibits a theoretical relationship between the displacement vector (system input), and z-axis-displacement vector (system output). The 3D coupling characteristics are analyzed in depth by investigating the interaction among the coupling variables in the model, and are further verified by a finite element simulation. Additionally, with the proposed model, the positioning method for the contact points and the corresponding calibration method are investigated in the spherical coordinate system, which is based on the assumption of direction consistency between the probing force and the spatial displacement of the stylus ball.