Analytic approximate formulas for flow and heat transfer through a porous medium in narrow crevices are derived. The Poiseuille number and the Nusselt number depend on the crevice geometry and the product of the aspect ratio and the porous medium factor, the latter being inversely proportional to the square root of the Darcy number. Exact numerical solutions show the approximate formulas are valid up to an aspect ratio of 0.3. The results are applicable to flow through porous rock fissures and biological clefts.