  The interaction between two-level systems (TLS) and strain fields in a solid
is contained in the diagonal matrix element of the interaction hamiltonian,
$\delta$, which, in general, has the expression $\delta=2[\gamma]:[S]$, with
the tensor $[\gamma]$ describing the TLS ``deformability'' and $[S]$ being the
symmetric strain tensor. We construct $[\gamma]$ on very general grounds, by
associating to the TLS two objects: a direction, $\hat\bt$, and a forth rank
tensor of coupling constants, $[[R]]$. Based on the method of construction and
on the invariance of the expression of $\delta$ with respect to the symmetry
transformation of the solid, we conclude that $[[R]]$ has the same structure as
the tensor of stiffness constants, $[[c]]$, from elasticity theory. In
particular, if the solid is isotropic, $[[R]]$ has only two independent
parameters, which are the equivalent of the Lam\'e constants. Employing this
model we calculate the absorption and emission rates of phonons on TLSs and
show that in isotropic solids, on average, the longitudinal phonons interact
stronger with the TLSs than the transversal ones, as it is observed in
experiments. We also show that in isotropic solids, a transversal wave leaves
unperturbed all the TLSs with the direction contained in one of the two planes
that are perpendicular either to the wave propagation direction or to the
polarization direction and that a longitudinal strain applied to the solid
polarises the TLS ensemble.
