  The existence and multiplicity of similarity solutions for the steady,
incompressible and fully developed laminar flows in a uniformly porous channel
with two permeable walls are investigated. We shall focus on the so-called
asymmetric case where the upper wall is with an amount of flow injection and
the lower wall with a different amount of suction. We show that there exist
three solutions designated as type $I$, type $II$ and type $III$ for the
asymmetric case. The numerical results suggest that a unique solution exists
for the Reynolds number $0\leq R<14.10$ and two additional solutions appear for
$R>14.10$. The corresponding asymptotic solution for each of the multiple
solutions is constructed by the method of boundary layer correction or matched
asymptotic expansion for the most difficult high Reynolds number case.
Asymptotic solutions are all verified by their corresponding numerical
solutions.
