We discuss the susceptibility third-rank tensor for second harmonic and sumfrequency generation, associated with low index surfaces of silicon (Si(001), Si(011) and Si(111)) from two different approaches: the Simplified Bond-Hyperpolarizablility Model (SBHM) and Group Theory (GT). We show that SBHM agrees very well with the experimental results for simple surfaces because the definitions of the bond vectors implicitly include the geometry of the crystal and therefore the symmetry group. However, for more complex surfaces it is shown that one can derive from GT the SBHM tensor, if Kleinman symmetry is allowed. OCIS codes: (240.4350) Nonlinear optics at surfaces; (240.6700) Surfaces; (190.4350) Nonlinear optics at surfaces R .In this work, we are going to represent a general third rank tensor as a 9 × 3 matrix divided into three matrix of dimensions 3 × 3. Hence, an explicit representation in this notation of a general third rank tensor ijk d (i, j, k = 1, 2, 3) is given in Eq. (3):