  This paper introduces a new family of mixed finite elements for solving a
mixed formulation of the biharmonic equations in two and three dimensions. The
symmetric stress $\bm{\sigma}=-\nabla^{2}u$ is sought in the Sobolev space
$H({\rm{div}}\bm{div},\Omega;\mathbb{S})$ simultaneously with the displacement
$u$ in $L^{2}(\Omega)$. Stemming from the structure of
$H(\bm{div},\Omega;\mathbb{S})$ conforming elements for the linear elasticity
problems proposed by J. Hu and S. Zhang, the
$H({\rm{div}}\bm{div},\Omega;\mathbb{S})$ conforming finite element spaces are
constructed by imposing the normal continuity of $\bm{div}\bm{\sigma}$ on the
$H(\bm{div},\Omega;\mathbb{S})$ conforming spaces of $P_{k}$ symmetric tensors.
The inheritance makes the basis functions easy to compute. The discrete spaces
for $u$ are composed of the piecewise $P_{k-2}$ polynomials without requiring
any continuity. Such mixed finite elements are inf-sup stable on both
triangular and tetrahedral grids for $k\geq 3$, and the optimal order of
convergence is achieved. Besides, the superconvergence and the postprocessing
results are displayed. Some numerical experiments are provided to demonstrate
the theoretical analysis.
