  The elastic $\pi N$ scattering is investigated for the $I=3/2$ channel
dominated by the $\Delta(1232)$ resonance at finite baryon density, employing
the effective Lagrangian approach at the tree-level Born approximation. The
quark-meson coupling (QMC) model is employed to describe the in-medium baryon
properties that are constructed at the quark level, such as the nucleon and
$\Delta$ masses, and $\Delta$ full decay width. I reproduce the experimental
data of the cross-section in a vacuum as a justification of our approach and
then analyze the in-medium total and differential cross-sections as well as
proton-spin asymmetry. Following the results of the in-medium elastic $\pi N$
scattering calculation, the elastic $\pi A$ scattering is investigated at
finite baryon density in the framework of the Eikonal Glauber model for the
light nuclei, $^4\mathrm{He}$ and $^{12}\mathrm{C}$. For the description of the
finite nuclei, the Wood-Saxon density profile, and an expansion of the charge
distribution as a sum of Gaussians are employed in this study. The nuclear
density distribution $\rho_A$, effective baryon mass $m^*_B$, in-medium decay
width $\Gamma^*_\Delta$, and in-medium coupling constants $f^*_{\pi NN}$ and
$f^*_{\pi N \Delta}$ are analyzed as well as the total cross-section. The
results show that the effective baryon mass and cross-sections in the medium
decrease as density increases except for the $\Delta$ decay width, which
increases as the density increases. The elastic $\pi A$ scattering at the
tree-level Born approximation reproduces well the experimental data for
$^4\mathrm{He}$ but overestimates for $^{12}\mathrm{C}$. Results for the
in-medium $\Delta$ resonance and other findings in this work will be relevant
for the relativistic heavy-ion collision experiments.
