  The modular product $G\diamond H$ of graphs $G$ and $H$ is a graph on vertex
set $V(G)\times V(H)$. Two vertices $(g,h)$ and $(g',h')$ of $G\diamond H$ are
adjacent if $g=g'$ and $hh'\in E(H)$, or $gg'\in E(G)$ and $h=h'$, or $gg'\in
E(G)$ and $hh'\in E(H)$, or (for $g\neq g'$ and $h\neq h'$) $gg'\notin E(G)$
and $hh'\notin E(H)$. We derive the distance formula for the modular product
and then describe all edges of the strong resolving graph of $G\diamond H$.
This is then used to obtain the strong metric dimension of the modular product
on several, infinite families of graphs.
