The effect of fine multilayered structuring on the resonant periods of global sausage ( m=0), fast magnetoacoustic oscillations of coronal loops is studied for the straight magnetic slab model filled with a zero- β plasma. The slab is considered to have a one-dimensional inhomogeneity of the Alfvén speed in the direction perpendicular to the axis of the slab, which coincides with the equilibrium, straight, magnetic field. This magnetic configuration models an oscillating coronal loop that is formed by a bundle of field-aligned, smooth, concentric, circular shells of variable density and width. The number of the layers (or shells), along with their density, width, and radial steepness, are randomly distributed. It is shown that the resonant properties of long-wavelength sausage standing modes of the slab are not sensitive to the details of fine structuring. It is concluded that the coronal seismological technique for the determination of the magnetic field strength by the period of global sausage oscillations is not sensitive to the fine multilayered or multishell structuring.