  We propose two families of mixed finite elements for solving the classical
Hellinger-Reissner mixed problem of the linear elasticity equations in three
dimensions. First, a family of conforming mixed triangular prism elements is
constructed by product of elements on triangular meshes and elements in one
dimension. The well-posedness is established for all elements with $k\geq1$,
which are of $k+1$ order convergence for both the stress and displacement.
Besides, a family of reduced stress spaces is proposed by dropping the degrees
of polynomial functions associated with faces. As a result, the lowest order
conforming mixed triangular prism element has 93 plus 33 degrees of freedom on
each element. Second, we construct a new family of nonconforming mixed
tetrahedral elements. The shape function spaces of our stress spaces are
different from those of the elements in literature.
