To solve the contradiction between speed and precision for a high speed mechanism, the flexible problem of a 3-RR-P parallel measuring machine was researched. On the basis of the elastic beam kinematics theory and Galerkin modal truncation method, a kinematics deformation model of one-dimensional elastic beam was established. Then, a flexible rod was assumed to be Euler-Bernoulli beam, the flexible structure coupling dynamics model considering the deformation of midline was built based on Hamilton principle. Finally, the measuring error generated by vibration of elastic beam was tested at different speeds based on midline coupling dynamics model. A method to reduce vibration coupling error by adjusting reasonably the viscous friction coefficient was proposed to improve the test accuracy. Experiment results show that the max lateral one-order coupling error is 28.6 μm when angular velocity comes to 300 rad/s in ignoring structure errors. Moreover, when viscous friction coefficient is adjusted to be 0.4-0.5, the vibration coupling error is reduced to less than 15 μm, reducing by 13.6 μm as compared to that of the previous adjustment. These data have been verified to be effective and feasible for solving the contradiction between high speed and high precision. It offers a foundation for research on the coupling principle between high order elastic vibration and accuracy.