The influence of mesoscale topography on the baroclinic instability of a two-layer model of the open ocean is considered. For westward velocities in the top layer (U), and for a sinusoidal topography independent ofxor longitude (a cross-stream topography), the critical value ofU(Uc) leading to instability is the same as when there is no topography. The wavelength of the unstable perturbation corresponding to Ucis shortened. For a given wavevector (k) of the perturbation the system becomes stable (as also in the absence of topography) for large values of |U|. The minimum value of the shear leading to stability is, however, significantly reduced by the topography.