Mechanisms of mass transfer into composite thin slabs consisting of two thin metal layers in perfect contact using the hyperbolic mass conduction model have been studied. The non-Fickian phenomena are analyzed by comparison of the solutions between Fickian and non-Fickian equations. The effects of diffusion ratio of carbon, density ratio, and thermal relaxation time on the spatial and transient behavior of the composite slabs are investigated semi-analytically using the Laplace transformation technique.