  Let $R$ be a commutative ring with identity. The co-maximal ideal graph of
$R$, denoted by $\Gamma(R)$, is a simple graph whose vertices are proper ideals
of $R$ which are not contained in the Jacobson radical of $R$ and two distinct
vertices $I, J$ are adjacent if and only if $I+J=R$. In this paper, we use
Gallai$^{^,}$s Theorem and the concept of strong resolving graph to compute the
strong metric dimension for co-maximal ideal graphs of commutative rings.
Explicit formulae for the strong metric dimension, depending on whether the
ring is reduced or not, are established.
