Two-Degree-Of-Freedom Vortex-Induced Vibration (VIV) of Two Rigidly Coupled Circular Cylinders of Different Diameters at a Low Reynolds Number of 250 is Investigated Numerically. While the Diameter Ratio and the Mass Ratio Are Kept Constant, the Study is Focused on the Effect of the Position Angle of the Small Cylinder on the Lock-In Regime of the VIV. Simulations Are Carried Out for Position Angles Α of the Small Cylinder Ranging from 0° to 180° with an Interval of 22.5° and the Reduced Velocities Ranging from 1 to 15 with an Increment of 1. in Order to Find the Effect of the Gap between the Two Cylinders on the Vibration, Two Gap-To-Diameter Ratios (0 and 0.2) Are Considered. It is Found that Compared with a Single Cylinder Case, the Lock-In Regime of the Reduced Velocity is Widened Significantly When the Position Angle of the Small Cylinder is Α = 0°, 22.5°, 90°, or 112.5°. Pulsed Beating Phenomenon Characterized by Regular Vibration with Occasional High-Amplitude Disturbances at Regular or Irregular Intervals is Observed at G = 0 and Α = 90°. at Α = 135°, More Than One Lock-In Regimes Are Observed in the Computed Range of Reduced Velocity for Both Gaps (G = 0 and 0.2). Setting a Small Gap (Gap-To-Diameter Ratio of 0.2) between the Two Cylinders Mitigates the Vibration by Narrowing the Lock-In Regime and Reducing the Vibration Amplitude. © 2013 AIP Publishing LLC.