Using a nonlinear critical layer analysis, we find a class of steady state, finite-amplitude waves in the Garcia model of an inviscid stratified shear layer. The vorticity distribution inside the vortex cores is similar to that of the family of two-dimensional vortices, known as Stuart vortices, found by Stuart (1967) in a homogeneous shear layer. The solutions obtained are compared with those previously obtained using similar techniques, but for which the Prandtl-Batchelor theorem had been invoked inside closed streamlines to justify the homogenization of vorticity therein.