In long rectangular Hele‐Shaw cells the Saffman‐Taylor instability generates steady advancing fingers of the less viscous fluid. The structure of these fingers is determined by the solution of a system of nonlinear integrodifferential equations for two unknown functions of the curvilinear coordinate defined along the boundary of the finger. The surface tension appears in these equations through a dimensionless coefficient calledk. I analyze the solution when this coefficient tends to infinity. In this limit, the inviscid fluid tends to fill almost completely the cell, except for a thin layer of viscous fluid left on the sides of thickness of order
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