Abstract: A furnace lining is composed of a plurality of layers of fiber insulation. The innermost layer is formed by stacking flat, elastically-compressible fibrous strips. The stacked strips are compressed and held down in compressed condition by a plurality of anchor members secured to and projecting perpendicularly from the furace wall and extending between selected strips of said innermost layer. The elastic compression applied to the strips creates a frictional grip between the strips and the anchor members, which maintains the lining in a stable mounted position. The lining may also include an intermediate layer between the innermost layer and the furnace wall, this intermediate layer being also formed of superimposed, strips stacked flat upon one another, with the intermediate layer frictionally anchored to the outermost layer.