We employ quantum mechanics modeling to investigate the effects of Ge and Si solute elements on the elastic properties and plastic deformation modes in two families of high-entropy alloys, CoCrFeMnNi and CoCrFeNi, and medium-entropy alloy, CoCrNi. The static lattice constants and single-crystal elastic parameters are calculated for these three face-centered-cubic random solid solutions as a function of composition. Using the elastic constants, we analyzed mechanical stability, derived polycrystalline modulus, and evaluated solid-solution strengthening for these multi-component alloys. We fabricated (CoCrFeNi)(100-x) Si-x (x = 0, 4, 6) and measured the polycrystalline modulus and hardness. The calculated trends for Young's and shear modulus as well as lattice parameters were verified by our measurements. The dependence of generalized stacking fault energy on Ge and Si was studied in detail for the considered multi-component alloys. The competition between various plastic deformation modes was revealed based on effective energy barriers. Our calculations predict that the activated deformation modes in all the alloys studied here are the stacking fault mode (dominant) and the full-slip mode (secondary), and as the concentrations of Ge and Si increase, twining becomes favored.