  In this paper, we study the stability of the nonsymmetric version of
Nitsche's method without penalty for compressible and incompressible
elasticity. For the compressible case we prove the convergence of the error in
the $H^1$- and $L^2$-norms. In the incompressible case we use a Galerkin least
squares pressure stabilization and we prove the convergence in the $H^1$-norm
for the velocity and convergence of the pressure in the $L^2$-norm.
