Hot embossing is a compression molding technique used for high replication accuracy of small features. One of the most sensitive phases of the process is the de-embossing stage during which the patterned part has to be demolded. In this paper, the demolding stage is considered as a frictional contact problem between a rigid mold insert and a viscoelastic polymer sheet as it deforms and cools inside a mold under an applied force. The contact is modeled with a modified Coulomb's law of dry friction while a generalized Maxwell model is used to describe the polymer behavior during embossing, cooling and de-embossing stages. The heat tran. fer between the mold insert and the patterned polymer sheet is solved through a domain decomposition method. A finite element approximation based on a penalized technique is proposed and analyzed. The purpose of this modeling approach is to predict dimensional stability and residual shape of microcomponents in the hot embossing process. Such a prediction will allow one to assign appropriate processing conditions that minimize geometrical imperfections and increase replication accuracy.