To understand the coupled motion between linear and rotational motion of 3-axis actuator, generalized actuator modeling was constructed, and from the planar vector model of actuator, expanded equation of motion, which could describe 3-axis motion was built. From the equation of motion, 3x3 transfer function matrix was obtained, and coupling behavior was observed. To analyze the coupling behavior, singular value decomposition of transfer function matrix was applied and led to the conclusion that rotational motion strongly influenced linear motion. Therefore, to obtain decoupling system, transfer function matrix should be a diagonal form, and in order to do so, decoupler was inserted in front of actuator plant model. Decoupler made the pseudo plant, which was composed of decoupler and original actuator plant as a diagonal form. To change actuator plant model, design variable was selected and optimal value range was confirmed. Sensitivity analysis was performed to get the critical variables, which affected coupling motion between linear and rotational direction.