  A strongly symmetric stress approximation is proposed for the Brinkman
equations with mixed boundary conditions. The resulting formulation solves for
the Cauchy stress using a symmetric interior penalty discontinuous Galerkin
method. Pressure and velocity are readily post-processed from stress, and a
second post-process is shown to produce exactly divergence-free discrete
velocities. We demonstrate the stability of the method with respect to a
DG-energy norm and obtain error estimates that are explicit with respect to the
coefficients of the problem. We derive optimal rates of convergence for the
stress and for the post-processed variables. Moreover, under appropriate
assumptions on the mesh, we prove optimal $L^2$-error estimates for the stress.
Finally, we provide numerical examples in 2D and 3D.
