Observations of the disturbed morphologies and internal velocity distr
ibutions, and of the relative positions, orientations, and centroid ve
locities of the interacting spiral galaxies IC 2163 and NGC 2207, are
reproduced by computer simulations of each galaxy. The ocular morpholo
gy of IC 2163, consisting of a bright oval with pointed apices and a d
ouble-parallel structure in the tidal arm, as well as the streaming mo
tions along the oval and the arms and the nearly perpendicular alignme
nt 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 N
GC 2207 that had a closest approach similar to 4 x 10(7) yr ago. In NG
C 2207, strong velocity anomalies consisting of a global distortion of
the velocity distribution into an S shape and a 40 degrees misalignme
nt of the kinematic and photometric minor axes are fitted by a dynamic
al model in which the companion, IC 2163, moved in a plane perpendicul
ar to the disk of NGC 2207 with the same relative orbit as in the IC 2
163 model. The resulting out-of-plane tidal forces are producing a war
p of the disk of NGC 2207 with present z-displacements as large as 9 k
pc and present z-velocities up to 100 km s(-1). The large southern ext
ension of NGC 2207 observed in H I and in optical images is probably a
tidal remnant from the time, similar to 2.4 x 10(8) yr ago, when IC 2
163 crossed the western extrapolated plane of NGC 2207 from the near s
ide to the far side, prior to perigalacticon on the far side. The high
resolution of both the observations and the models gives an unprecede
nted view of the dynamics of strong tidal interactions between galaxie
s.