  We study the BMN correspondence between certain Penrose limits of type IIB
superstrings on pp-wave orbifolds with $ADE$ geometries, and the set of
four-dimensional $\mathcal{N}=2$ superconformal field theories constructed as
quiver gauge models classified by finite $ADE$ Lie algebras and affine
$\hat{ADE}$ Kac-Moody algebras. These models have 16 preserved supercharges and
are based on systems of D3-branes and wrapped D5- and D7-branes. We derive
explicitly the metrics of these pp-wave orbifolds and show that the BMN
extension requires, in addition to D5-D5 open strings in bi-fundamental
representations, D5-D7 open strings involving orientifolds with $Sp(N)$ gauge
symmetry. We also give the correspondence rule between leading string states
and gauge-invariant operators in the $\mathcal{N}=2$ quiver gauge models.
