Scaling devices that can shrink or enlarge an object are designed using transformation optics. The electromagnetic scattering properties of such scaling devices with anisotropic parameters are rigorously analyzed using the eigenmode expansion method. If the radius of the virtual object is smaller than that of the real object, it is a shrinking device with positive material parameters; if the radius of the virtual object is larger than the real one, it is an enlarging device with positive or negative material parameters. Hence, a scaling device can make a dielectric or metallic object look smaller or larger. The rigorous analysis shows that the scattering coefficients of the scaling devices are the same as those of the equivalent virtual objects. When the radius of the virtual object approaches zero, the scaling device will be an invisibility cloak. In such a case, the scattering effect of the scaling device will be sensitive to material parameters of the device.