The stratified shear flow over a two-dimensional obstacle of semi-elliptical crosssection is considered. The shear flow is assumed to be inviscid with constant upstream values of the density gradient and dynamic pressure (Long's model). Two complete sets of lee-wave functions, each of which satisfies the condition of no upstream reflexion, are determined in elliptic co-ordinates for E 2 1 and E < 1, where E is the ratio of height to half-width of the obstacle. These functions are used to

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... ne the lee-wave field produced by, and the consequent drag on, a semi-elliptical obstacle as functions of E and the reduced frequency (reciprocal Froude number) within the range of stable flow. The reduced frequency at which static instability first occurs is calculated as a function of 8.