Electric field applied to silicon, which is a kind of centrosymmetric materials, induces effective even-order nonlinear susceptibilities for silicon due to the vanishing of its inversion symmetry. The tensors of effective second-order susceptibilities of silicon are systematically studied according to the theories of χ(2)eff=χ(3)·E and tensor transformation when the directions of the applied electric fields or the built-in fields in the bulk of silicon crystal are along the crystal orientations of [111], [110] and [001], respectively. The results show that the forms of effective second-order susceptibilities agree with those of point groups of C3v, C2v and C4v, respectively, which indicates that silicon single crystal should belong to C3v, C2v or C4v group instead of Oh group under corresponding electric field, and thus, it should possess second-order nonlinear optical properties corresponding to related symmetric crystal. Also, a general deduction of χ(2)eff for silicon under an arbitrary applied electric field E is proposed, which can provide theoretical fundamentals for electric field-induced second-order nonlinear optical experiments of silicon and for those of other centrosymmetric materials.