  Matrix elements of the form $ <0| Tr \; g^{2}GG |G> $ are calculated using
the lattice QCD Monte Carlo method. Here, $|G>$ is a glueball state with
quantum numbers $ 0^{++}$, $ 2^{++}$, $ 0^{-+}$ and $G$ is the gluon field
strength operator. The matrix elements are obtained from the hybrid correlation
functions of the fuzzy and plaquette operators performed on the $12^{4}$ and
$14^{4}$ lattices at $\beta = 5.9 $ and $5.96$ respectively. These matrix
elements are compared with those from the QCD sum rules and the tensor meson
dominance model. They are the non-perturbative matrix elements needed in the
calculation of the partial widths of $J/\Psi$ radiative decays into glueballs.
