Built-in Eccentric Bearing-Torsional Spring (BEBTS) type Automatic Belt Tension Unit (ABTU) is one of typical belt tension units. The BEBTS type ABTU system frequently experiences torsional vibration about its pivot due to the variation of belt tension. However, it is very difficult to analyze the rotational (or torsional) vibration of the ABTU because the exciting moment varies according to the change of belt tension. To get over this difficulty, in this paper. the ABTU was simplified as 1-DOF translational motion model in the tangential direction. Its equation of motion was derived and solved. The time history and frequency responses were computed and examined for three of BEBTS type ABTUs which are made by different manufacturers but the tame kind.