  We study the quantitative unique continuation property of some higher order
elliptic operators. In the case of $P=(-\Delta)^m$, where $m$ is a positive
integer, we derive lower bounds of decay at infinity for any nontrivial
solutions under some general assumptions. Furthermore, in dimension 2, we can
obtain essentially sharp lower bounds for some forth order elliptic operators,
the sharpness is shown by constructing a Meshkov type example.
