The dynamics of gas in the disk of the SBc galaxy NGC 3359 are studied by means of hydrodynamical simulations. These models are compared to the observed structure and kinematics of neutral hydrogen in the galaxy, as mapped with a resolution of 1 kpc at the VLA. Near-infrared surface photometric observations of the stellar bar are used to constrain models further. The most successful models reproduce the essentials of the observed gaseous spiral structure in both its distribution and kinematics. However, this success is achieved only by arbitrarily imposing an oval distortion potential which does not correspond to the shape of the observed stellar bar. Models using only a bar derived from the surface photometry are unable to generate spiral structure of the required amplitude in the outer parts of the galactic disk, because the physical bar is too short and its forces fall off too rapidly. The essential role of the oval distortion in the more successful models seems to be maintenance of a significant tangential force on the gas well out into the disk. We offer brief speculations on what might fill a similar role in the physical galaxy: leading candidates are various types of spiral wave, for which the oval distortion may act as a proxy, or possibly a global mode of the galaxy's disk.