Performance enhancement of strained Si material originates from the stress on it, which can be measured by Raman spectroscopy. A study of the theoretical model of strain-induced Raman spectrum frequency shift in strained Si material is of profound theoretical and practical significance. The Raman frequency shift of strained Si is significantly correlated with the stress intensity, the stress type and the crystal plane. However, the corresponding reports republished are lacking in integrality and systematization in the process of modeling. In this paper, according to the theory of Raman spectroscopy, based on Secular equation and Raman selection rules, quantitative relationships between strain tensor and Raman frequency shift for uniaxial and biaxial strained Si grown on (001), (101), and (111) SiGe substrates are achieved. On this basis, theoretical models of mechanical stress and Raman spectrum for uniaxial and biaxial strained Si materials grown on (001), (101), and (111) SiGe substrates are obtained using Hooke's law, respectively. The procedure for setling up these models is elaborate and systematic and the results obtained are comprehensive and quantificational, which can provide an important reference for the stress analysis in strained Si material.