  Let $f:A\lo B$ be a ring homomorphism and let $J$ be an ideal of $B.$ In this
paper, we investigate the transfer of notions elementary divisor ring, Hermite
ring and B\'ezout ring to the amalgamation $A\bowtie^fJ.$ We provide necessary
and sufficient conditions for $ A\bowtie^fJ$ to be an elementary divisor ring
where $A$ and $B$ are integral domains. In this case it is shown that $
A\bowtie^fJ$ is an Hermite ring if and only it is a B\'ezout ring. In
particular, we study the transfer of the previous notions to the amalgamated
duplication of a ring $A$ along an $A-$submodule $E$ of $Q(A)$ such that
$E^2\subseteq E.$
