  We study the transverse oscillatory modes of nanomechanical silicon nitride
strings under high tensile stress as a function of geometry and mode index m <=
9. Reproducing all observed resonance frequencies with classical elastic theory
we extract the relevant elastic constants. Based on the oscillatory local
strain we successfully predict the observed mode-dependent damping with a
single frequency independent fit parameter. Our model clarifies the role of
tensile stress on damping and hints at the underlying microscopic mechanisms.
