we give a geometric analog of the weil representation of the metaplectic group, placing it in the framework of the geometric langlands program. for a smooth projective curve $x$ we introduce an algebraic stack bun$\backsim$g of metaplectic bundles on $x$. we give a tannakian description of the langlands dual to the metaplectic group. namely, we introduce a geometric version sph of the (nonramified) hecke algebra of the metaplectic group and describe it as a tensor category. the tensor category sph acts on the derived category d(bun$\backsim$g) by hecke operators. further, we construct a perverse sheaf on bun$\backsim$g corresponding to the weil representation and show that it is a hecke eigensheaf with respect to sph.