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We study the structure of the indecomposable direct summands of tensorproducts of two restricted simple $SL_3(K)$-modules, where $K$ is analgebraically closed field of characteristic $p \geq 5$. We give acharacteristic-free algorithm for the computation of the decomposition of sucha tensor product into indecomposable modules.  The $p<5$ case for $\SL_3(K)$ was studied in the authors' earlier paper. Inthis paper we show that for characteristics $p\geq 5$ all the indecomposablesummands are rigid, in contrast to the situation in characteristic 3.

Decomposition of Tensor Products of Modular Irreducible Representations for $SL_3$: the $p \geq 5$ case