A special analytical solution is derived for the classical orographic configuration of two-dimensional, stratified, linear, non-hydrostatic and dry model (without friction and Coriolis force). The well-known differential equation for the vertical velocity involves the vertical distribution of the Scorer parameterl 2(z) and in this casel 2 is specified such that the lower atmosphere has a stable duct near the surface and is capped by a layer which acts as a good reflector. Examination of the solution for the vertical amplitude in the vicinity of singularities indicates the dominant lee wavelength and observations confirm that in comparable settings resonant trapped gravity waves develop in the lee of mountains. Comparison with a real atmospheric lee-wave events gives good predictions for the wavelength and wave drag, but, as in other linear models, the amplitude is underestimated.