In this paper, based on the framework of kp method, the influence of uniaxial stress on the conduction band energy-band structure of bulk-Si is analysed first, the coupling of 1 and 2 bands at the X point, and the influence of that band-band coupling on the minimum of energy valley are then separately discussed under the action of shear strain. On that basis, the dispersion relation close to the minimum is obtained. Furthermore, the different valley orientations need to be taken into account. Using the coordinate transformation, the modelling for dispersion relation of each valley with arbitrary uniaxial stress is finally achieved. The proposed analytical model in this paper is also suited to the understanding of the physical properties of uniaxial strained Si material and may provide some references for the study on bandstructure and electrical properties of the inversion layer in uniaxial strained Si nMOSFETs.