  Radio-bright, presumably young supernova remnants offer the opportunity of
studying strong-shock physics and the nature of the interaction of ejected
material with the surrounding medium. We use VLA and ROSAT images of the
radio-bright supernova remnant 3C 397 (G41.1--0.3) to examine the shock
structure in both thermal X-ray emission and nonthermal radio emission. The
unusual rectangular morphology can be seen in VLA maps at 20 and 6 cm
wavelength at a resolution of 6", and in ROSAT HRI images. The X-ray images
resemble the radio strongly, except for a small, possibly un resolved X-ray hot
spot near the center. There is no variation in the X-ray hardness ratio from
ROSAT Position Sensitive Proportional Counter data across the remnant,
suggesting that at least between 0.4 and 2 keV, the interior emission is not
different in character from that in the bright shell regions. Thus 3C 397 is
not a member of the ``thermal composite'' or ``mixed-morphology'' class (Rho
1998). The remnant is unpolarized at 20 cm, and has a mean fractional
polarization of 1.5% +/- 0.1% at 6 cm. The polarized flux, and polarized
fraction, peak inside the remnant at a location not coincident with either an
internal maximum in total-intensity radio emission, or with the X-ray hot spot.
Spectral-index maps between 6 and 20 cm do not show any systematic differences
associated with interior emission; there appears to be no ``plerionic'' or
pulsar-driven component in 3C 397 at least as normally characterized by high
polarization and a flat radio spectrum. Spectral-index values spread about the
mean by about 0.2, a result consistent with previous work. We make calculations
of the upstream electron diffusion coefficient and the mean density. Finally,
we speculate on possible mechanisms producing the X-ray hot spot.
