Based on the poly-electron fine structure Hamiltonian and irreducible tensor theory, and considering the exchange interaction between electrons and the different shielding effects of inner and outer shell electrons, a successful derivation can be achieved of the analytical expressions of non-relativistic and relativistic corrections for neutral silicon atoms and lowly-charged silicon-like ions Z=14~17 levels, followed by an analysis of the contributions of various relativistic corrections, which results are in good agreement with the experimental measurements.