Shell-like free volume theory for multicomponent polymeric systems was developed. Molecular-diffusive motion in polymeric systems is due to a large number of microscopic molecular collisions with adjacent molecules. To embody this idea, a shell-like free volume is defined as the free space surrounding the penetrant molecule that emerges from molecular collisions. The common description of molecular collisions allows the shell-like free volume theory to include multicomponent systems. An advantage of the theory is it can estimate molecular self-diffusivity in multicomponent polymeric systems using only pure component parameters of the constituents and no arbitrary parameter or empirical equation. The required parameters can be derived from viscoelastic properties and quantum chemical calculations. Moreover, by comparing experimental and theoretical values, we find that, insofar as no strong interaction is included, this model can fairly predict penetrant self-diffusivities in several multicomponent systems with a wide range of compositions and different types of molecules, even though the model contains no adjustable parameters.