This talk 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 is sought in the space H(divdiv) simultaneously with the displacement in L2. Stemming from the structure of H(div) conforming elements for the linear elasticity problems proposed by Hu and Zhang, the H(divdiv) conforming finite element spaces are constructed by imposing the normal continuity of divergence on the H(div) conforming spaces of piecewise symmetric matrix valued polynomials of degree not more than k. The inheritance makes the basis functions easy to compute. The discrete spaces for the displacement are composed of piecewise polynomials of degree not more than k-2 without requiring any continuity. Such mixed finite elements are inf-sup stable on both triangular and tetrahedral grids for polynomial degree not less than 3, and the optimal order of convergence is achieved