The equilibrium geometries and energies of neutral BeSin (n = 2-10) species and their anions have been studied at the highest level of Gaussian-3 (G3) theory. The results reveal that the ground-state structures of these clusters are Be-encapsulated in silicon cages with n >= 8. The reliable adiabatic electron affinities of BeSin have been predicted to be 1.68 eV for BeSi2, 1.87 eV for BeSi3, 2.33 eV for BeSi4, 2.29 eV for BeSi5, 2.11 eV for BeSi6, 2.37 eV for BeSi7, 2.95 eV for BeSi8, 2.74 eV for BeSi9, and 1.92 eV for BeSi10. The dissociation energies of Be atom from BeSin, Si atom from BeSin, and Si atom from Si-n Clusters have also been calculated, respectively, to examine relative stabilities. The trend of stability of BeSin changed with n is converse to that of Si-n when n <= 7. From n >= 8, the encapsulated Be atom in silicon cages not only results in an identical trend for stability of BeSin and Si-n but also improves the stability Of Si-n clusters.