Observations of the disturbed morphologies and internal velocity distributions, and of the relative positions, orientations, and centroid velocities of the interacting spiral galaxies IC 2163 and NGC 2207, are reproduced by computer simulations of each galaxy. The ocular morphology of IC 2163, consisting of a bright oval with pointed apices and a double-parallel structure in the tidal arm, as well as the streaming motions along the oval and the arms and the nearly perpendicular alignment of the kinematic and photometric minor axes, are fitted to a model in which IC 2163 is reacting to an in-plane, prograde encounter with NGC 2207 that had a closest approach ˜4 × 107 yr ago. In NGC 2207, strong velocity anomalies consisting of a global distortion of the velocity distribution into an S shape and a 40 misalignment of the kinematic and photometric minor axes are fitted by a dynamical model in which the companion, IC 2163, moved in a plane perpendicular to the disk of NGC 2207 with the same relative orbit as in the IC 2163 model. The resulting out-of-plane tidal forces are producing a warp of the disk of NGC 2207 with present z-displacements as large as 9 kpc and present z-velocities up to 100 km s-1. The large southern extension of NGC 2207 observed in H I and in optical images is probably a tidal remnant from the time, ˜2.4 × 108 yr ago, when IC 2163 crossed the western extrapolated plane of NGC 2207 from the near side to the far side, prior to perigalacticon on the far side. The high resolution of both the observations and the models gives an unprecedented view of the dynamics of strong tidal interactions between galaxies.