Flow-induced vibrations of two side-by-side circular cylinders are numerically studied using the immersed boundary method for Reynolds numbers of 60-200. The two cylinders are constrained to vibrate only in the transverse direction. The center-to-center spacing ratio (s/D) is in the range 2.0-5.0, and the reduced velocity (Ur) is in the range 2.0-10.0. The smallest increments for s/D and Ur are 0.02 and 0.01, respectively. It was found that the vibration amplitudes, mean position shifts, lift and drag forces, spectral frequencies, and phase lags between the lift and displacement are significantly influenced by s/D and Ur, supported by (a) a wider lock-in region compared to the case of a single cylinder, (b) emergence of asymmetric vibration where the amplitudes of two cylinders are not identical, (c) the phase jump between the lift and displacement resulting from multiple harmonic frequencies, and (d) a significant drop in mean position shift accompanied by the changes in the frequency or wake pattern. Furthermore, the influences of the spacing ratio, Reynolds number, blockage ratio, and mass ratio, on asymmetric vibration with single-sided hysteresis (AV-I), are examined in detail. The AV-I with double-sided hysteresis was confirmed for the first time when the cylinder mass ratio is larger than 5.0.