An apparatus for draping knitted fiber fabrics for curved profiled structural parts of fiber composite material includes a mold having a mold surface that corresponds to a portion of the desired profile geometry and curvature of the profiled structural part, a clamping device for tensioning a layer of a knitted fiber fabric along a tensioning line in a prestressed state, and a movement device for producing a relative movement between the mold and the clamped-in fabric layer such that the mold surface moves close to the fabric layer in a direction perpendicular to the tensioning line and, in the further course of the relative movement, pushes through the tensioning line such that the fabric layer completely covers the mold surface. The clamping device is equipped to load the fabric layer during the entire draping operation with a tensile force acting along the tensioning line.