  We present a higher order stabilization-free virtual element method applied
to plane elasticity problems. We utilize a serendipity approach to reduce the
total number of degrees of freedom from the corresponding high-order
approximations. The well-posedness of the problem is numerically studied via an
eigenanalysis. The method is then applied to several benchmark problems from
linear elasticity and we show that the method delivers optimal convergence
rates in $L^2$ norm and energy seminorm that match theoretical estimates as
well as the convergence rates from higher order virtual element methods.
