The present study focuses on out-of-plane and in-plane vibrations of sluice gates due to the fluid–structure interaction based on numerical modelling, using the finite-element method. Primarily, the vibration of the gate was restricted to a single direction, detaching the horizontal and vertical vibrations of the gate so as to exclude their interaction. Results indicated that, if the edge of the gate is bevelled at an angle of 45°, the lowest amplitudes of horizontal vibrations are obtained. Whereas the maximum horizontal vibrations are associated with the uppermost values of the reduced velocities, for example v_r > 3·5, as well as the gate's normalised opening height δ/d of about 0·8, the maximum vertical vibrations are attained for intermediate values of v_r, at about 3, and δ/d = 0·8. If both the horizontal and vertical vibrations are mutually considered, the two-dimensional reduced velocities v_rx and v_ry and the structural natural frequencies f_x and f_y become relatively different compared to these of single-way vibrations. Results also indicated that the amplitudes of the horizontal vibrations in the authors' previous analyses were considerably greater than those of single-way horizontal vibrations. The maximum amplitude of the horizontal vibrations was observed to be close to the out-of-plane natural frequency, when 3·5 < v_rx < 7 and v_ry > 10. For vibration frequencies close to the vertical natural frequency f_y, however, the dominant vertical vibrations occur for 2 < v_ry < 4.