The response of gas to an ovally deformed gravitational potential or a weak bar of a disc galaxy is investigated by the implicit Osher upwind scheme with second-order of accuracy in space and a 180\(\times 180\) polar grid. Flow patterns obtained are sensitive to the pattern speed and the degree of a distortion from the axisymmetric part of the gravitational potential. Tightly wound spiral patterns were obtained even with a non- axisymmetric perturbation whose amplitude was as low as 0.01. Not only trailing arms but also leading arms are obtained in the inner region of model galaxies. When the amplitude of the non-axisymmetric perturbation is 0.05, we obtained loosely wound spirals.