The finite element method is used to simulate the near-wake of an elliptical cylinder undergoing rotationally oscillating motion at low Reynolds number, 50 ≤ Re ≤ 150. Reynolds number is based on equivalent diameter of the ellipse. The rotationally oscillating motion was carried out by varying the angle of attack between 10 deg and 60 deg, while the considered oscillation frequencies are between St/4 and 4 × St, where St is the Strouhal number of a stationary elliptical cylinder with zero angle of attack. Fluid flow results are presented in terms of lift and drag coefficients for rotationally oscillating case. The details of streamlines and vorticity contours are also presented for a few representative cases. The result indicates that at when the frequency is equal to the Strouhal number, the root-mean-square (RMS) of lift coefficient reaches its local minimum, while the average of drag coefficient reaches its local maximum. Increasing the Reynolds number increases the RMS of lift coefficient and decreases average of drag coefficient.