  The existence and stability conditions of Einstein static universe against
homogeneous scalar perturbations in the context of Lyra geometry is
investigated. The stability condition is obtained in terms of the constant
equation of state parameter $\omega=p/\rho$ depending on energy density
$\rho_0$ and scale factor $a_0$ of the initial Einstein static universe. Also,
the stability against vector and tensor perturbations is studied. It is shown
that a stable Einstein static universe can be found in the context of Lyra
geometry against scalar, vector and tensor perturbations for suitable range and
values of physical parameters.
