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In a previous work \cite{An1} matter models such that the energy density$\rho\geq 0,$ and the radial- and tangential pressures $p\geq 0$ and $q,$satisfy $p+q\leq\Omega\rho, \Omega\geq 1,$ were considered in the context ofBuchdahl's inequality. It was proved that static shell solutions of thespherically symmetric Einstein equations obey a Buchdahl type inequalitywhenever the support of the shell, $[R_0,R_1], R_0>0,$ satisfies $R_1/R_0<1/4.$Moreover, given a sequence of solutions such that $R_1/R_0\to 1,$ then thelimit supremum of $2M/R_1$ was shown to be bounded by$((2\Omega+1)^2-1)/(2\Omega+1)^2.$ In this paper we show that the hypothesisthat $R_1/R_0\to 1,$ can be realized for Vlasov matter, by constructing asequence of static shells of the spherically symmetric Einstein-Vlasov systemwith this property. We also prove that for this sequence not only the limitsupremum of $2M/R_1$ is bounded, but that the limit is$((2\Omega+1)^2-1)/(2\Omega+1)^2=8/9,$ since $\Omega=1$ for Vlasov matter.Thus, static shells of Vlasov matter can have $2M/R_1$ arbitrary close to$8/9,$ which is interesting in view of \cite{AR2}, where numerical evidence ispresented that 8/9 is an upper bound of $2M/R_1$ of any static solution of thespherically symmetric Einstein-Vlasov system.Comment: 20 pages, Late

On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System