  We report resonant ultrasound spectroscopy (RUS),
dilatometry/magnetostriction, magnetotransport, magnetization, specific heat,
and $^{119}$Sn M\"ossbauer spectroscopy measurements on SnTe and
Sn$_{0.995}$Cr$_{0.005}$Te. Hall measurements at $T=77$ K indicate that our
Bridgman-grown single crystals have a $p$-type carrier concentration of $3.4
\times 10^{19}$ cm$^{-3}$ and that our Cr-doped crystals have an $n$-type
concentration of $5.8 \times 10^{22}$ cm$^{-3}$. Although our SnTe crystals are
diamagnetic over the temperature range $2\, \text{K} \leq T \leq 1100\,
\text{K}$, the Cr-doped crystals are room temperature ferromagnets with a Curie
temperature of 294 K. For each sample type, three-terminal capacitive
dilatometry measurements detect a subtle 0.5 micron distortion at $T_c \approx
85$ K. Whereas our RUS measurements on SnTe show elastic hardening near the
structural transition, pointing to co-elastic behavior, similar measurements on
Sn$_{0.995}$Cr$_{0.005}$Te show a pronounced softening, pointing to
ferroelastic behavior. Effective Debye temperature, $\theta_D$, values of SnTe
obtained from $^{119}$Sn M\"ossbauer studies show a hardening of phonons in the
range 60--115K ($\theta_D$ = 162K) as compared with the 100--300K range
($\theta_D$ = 150K). In addition, a precursor softening extending over
approximately 100 K anticipates this collapse at the critical temperature, and
quantitative analysis over three decades of its reduced modulus finds $\Delta
C_{44}/C_{44}=A|(T-T_0)/T_0|^{-\kappa}$ with $\kappa = 0.50 \pm 0.02 $, a value
indicating a three-dimensional softening of phonon branches at a temperature
$T_0 \sim 75$ K, considerably below $T_c$. We suggest that the differences in
these two types of elastic behaviors lie in the absence of elastic domain wall
motion in the one case and their nucleation in the other.
