We consider the coupling across an interface of uid and porous media o ws with Beavers-Joseph- Saffman transmission conditions. Under an adequate choice of Lagrange multipliers on the interface we analyze inf-sup conditions and optimal a priori error estimates associated with the continuous and discrete formulations of this Stokes-Darcy system. We allow the meshes of the two regions to be non-matching across the interface. Using mortar nite element analysis and appropriate scaled norms we show that the constants that appear on the a priori error bounds do not depend on the viscosity, permeability and ratio of mesh parameters. Numerical experiments are presented. 1. Introduction. We analyze the coupling across an interface of uid and porous media o ws. This problem appears in several applications like well-reservoir coupling in petroleum engineering, transport of substances across groundwater and surface water, and (bio)uid- organ interactions. More precisely, we consider the following situation: an incompressible uid in a region can o w both ways across an interface into a saturated porous medium domain . The model studied here consists of Stokes equations in the uid region and Darcy law for the ltration velocity in the porous medium region . The transmission con- ditions we consider on the interface are the Beavers-Joseph-Saffman conditions (3, 19, 27) which are widely accepted by the scientic community. In this paper we study inf-sup condi- tions and a priori error estimates associated with the continuous and discrete formulations of