A flat eddy is defined by the condition &egr;=&dgr;/l≪1, wherel=(l−21+l−23)−1/2, andl1,l3, and &dgr; are the streamwise, spanwise, and vertical scales of the eddy, respectively. An approximate solution of the initial value problem for the evolution of a flat eddy in an inviscid flow is obtained using a Lagrangian formulation together with an expansion of the Euler equations in a Taylor series in time. The effects of horizontal pressure gradients on the eddy evolution are found to be small for small times such that &egr;U0t/l≪1, whereU0is a measure of the initial horizontal velocity. Nonuniformity of the spanwise stretching rate, together with the shearing of the eddy by the mean flow, is found to lead to the formation of internal shear layers, also when such layers were absent initially. The separate contributions to the streamwise fluctuation velocity due to redistribution of background momentum and direct driving by the pressure gradient are compared; the latter is found to be significantly smaller than the former and plays very little role in the shear layer formation process.