  We present and analyze a hybridizable discontinuous Galerkin (HDG) finite
element method for the coupled Stokes--Biot problem. Of particular interest is
that the discrete velocities and displacement are $H(\text{div})$-conforming
and satisfy the compressibility equations pointwise on the elements.
Furthermore, in the incompressible limit, the discretization is strongly
conservative. We prove well-posedness of the discretization and, after
combining the HDG method with backward Euler time stepping, present a priori
error estimates that demonstrate that the method is free of volumetric locking.
Numerical examples further demonstrate optimal rates of convergence in the
$L^2$-norm for all unknowns and that the discretization is locking-free.
