The self-diffusion anisotropy of n-hexane, n-heptane, n-octane, and n-decane in uniaxially compressed natural rubber samples with different cross-link densities was detected by pulsed-gradient stimulated spin-echo NMR. The effective diffusion coefficients and the displacement probabilities of alkane penetrant molecules were measured along and perpendicular to the direction of the compression force. For all solvents, the diffusion anisotropy increases with increasing compression. The microscopic theory of diffusion on the basis of the free volume is adapted to predict the dependence of the diffusion anisotropy on the deformation ratio. The theoretical dependence is in good agreement with the measurements on toluene and n-hexane swollen in cross-linked natural rubber samples. The anisotropy of diffusion of small penetrant molecules in elastomers could be used for NMR investigation of the deformation of polymer networks by the changes in the shape of the free volume.