  We present the temperature dependence of shear and longitudinal elastic
constants in a'-NaV2O5. For the longitudinal c22 and c33 modes we find
anomalies at Tc in contrast to the Spin Peierls substance CuGeO3 where only the
longitudinal mode along the chain shows a pronounced effect at TSP. The c66
shear mode (propagation along the chain in b-direction polarization in
a-direction) shows strong softening of 12%. Such a large effect is absent for
all shear modes in CuGeO3. We can interpret this softening with a coupling of
the exy symmetry strain to the charge fluctuation of B1g symmetry. We give the
possible low temperature charge distribution.
