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A finite element model (FEM) of elastic noise control materials like polyurethane foams is presented in this paper, and its implementation in two-dimensional form as a computer program is discussed. So that realistic noise control treatments could be studied, methods for coupling the foam FEM with conventional acoustical and structural finite elements are also described. The validity of the foam FEM is demonstrated by computing the sound absorption and transmission characteristics of simple coupled air/foam/panel systems and by comparing the results with existing experimental and analytical results for such arrangements. The FEM has been used to show that the constraint of a foam layer at its edge stiffens the foam acoustically. In addition, it has been found that the constraint of the ends of the facing panels in a foam-lined double panel system increases the sound transmission loss significantly at low frequencies.