  This paper proposes and analyzes a class of new weak Galerkin (WG) finite
element methods for 2- and 3-dimensional linear elasticity problems. The
methods use discontinuous piecewise-polynomial approximations of degrees
$k(\geq 0)$ for the stress, $k+1$ for the displacement, and a continuous
piecewise-polynomial approximation of degree $k+1$ for the displacement trace
on the inter-element boundaries, respectively. After the local elimination of
unknowns defined in the interior of elements, the WG methods result in SPD
systems where the unknowns are only the degrees of freedom describing the
continuous trace approximation. We show that the proposed methods are robust in
the sense that the derived a priori error estimates are optimal and uniform
with respect to the Lam\'{e} constant $\lambda$. Numerical experiments confirm
the theoretical results.
