Two-dimensional flow over a pair of circular cylinders in a side-by-side arrangement at low Reynolds numbers has been numerically investigated in this study Numerical simulations are performed, using the immersed boundary method, for the ranges of 40$leq$Re$leq$160 and $g^{*}$＜5, where Re and $g^{*}$ are, respectively, the Reynolds number and the spacing between the two cylinder surfaces divided by the cylinder diameter. Results show that a total of six kinds of wake patterns are observed over the ranges: antiphase-synchronized, inphase-synchronized, flip-flopping, single bluff-body, deflected, and steady wake patterns. It is found that the characteristics of the flow significantly depends both on the Reynolds number and gap spacing, with the latter much stronger than the former. Instantaneous flow fields, time traces, flow statistics and so on are presented to identify the wake patterns and then to understand the underlying mechanism. Moreover, the bifurcation phenomenon where either of two wake patterns can occur is found at certain flow conditions.ons.