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In this paper we study the geometry of the special fiber of Pappas-Rapoportmodels of Shimura varieties in the Hilbert case. More precisely we prove thatthe stratification induced by the Hodge polygon is a good stratification, whichis false in the Hilbert-Siegel case for $g\geq 2$. Then we use known results onthe convolution product of affine Grassmannians to describe the dimension ofthe strata and obtain that the forgetting morphism to the Kottwitz PEL model isflat in restriction to Hodge strata.

Stratification des vari\'et\'es de Hilbert en pr\'esence de ramification