  Using a generalized model of interaction between a two-level system (TLS) and
an arbitrary deformation of the material, we calculate the interaction of Lamb
modes with TLSs in amorphous nanoscopic membranes. We compare the mean free
paths of the Lamb modes with different symmetries and calculate the heat
conductivity $\kappa$. In the limit of an infinitely wide membrane, the heat
conductivity is divergent. Nevertheless, the finite size of the membrane
imposes a lower cut-off for the phonons frequencies, which leads to the
temperature dependence $\kappa\propto T(a+b\ln T)$. This temperature dependence
is a hallmark of the TLS-limited heat conductance at low temperature.
