  For any strong smash product algebra $A\#_{_R}B$ of two algebras $A$ and $B$
with a bijective morphism $R$ mapping from $B\ot A$ to $A\ot B$, we construct a
cylindrical module $A\natural B$ whose diagonal cyclic module
$\Delta_{\bullet}(A\natural B)$ is graphically proven to be isomorphic to
$C_{\bullet}(A\#_{_R}B)$ the cyclic module of the algebra. A spectral sequence
is established to converge to the cyclic homology of $A\#_{_R}B$. Examples are
provided to show how our results work. Particularly, the cyclic homology of the
Pareigis' Hopf algebra is obtained in the way.
