  In this paper we analyze a virtual element method for the two dimensional
elasticity problem allowing small edges. With this approach, the classic
assumptions on the geometrical features of the polygonal meshes can be relaxed.
In particular, we consider only star-shaped polygons for the meshes. Suitable
error estimates are presented, where a rigorous analysis on the influence of
the Lam\'e constants in each estimate is presented. We report numerical tests
to assess the performance of the method.
