  We provide a direct proof of Weyl's law for the buckling eigenvalues of the
biharmonic operator on a wide class of domains of $\mathbb R^d$ including
bounded Lipschitz domains. The proof relies on asymptotically sharp lower and
upper bounds that we develop for the Riesz mean $R_2(z)$. Lower bounds are
obtained by making use of the so-called "averaged variational principle". Upper
bounds are obtained in the spirit of Berezin-Li-Yau. Moreover, we state a
conjecture for the second term in Weyl's law and prove its correctness in two
special cases: balls in $\mathbb R^d$ and bounded intervals in $\mathbb R$.
