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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 todoi:10.1017/s0022112069001236 fatcat:togv6sypkze6pb6e2u2ulzxity