The strain tensor arising from uniaxial stress along an arbitrary direction on the (001) surface of Si is calculated. With these uniaxial strain tensor, the band structure of silicon material under arbitrary uniaxial stress on the (001) surface is calculated using K ·P perturbation theory coupled with linear deformation potential theory. The relation between energy band structure and stress parameters (type, direction, magnitude) was obtained. Finally, the uniaxial stress induced band structure change, such as that of the conduction band (CB) and the valence band (VB) edge levels, CB and VB splitting energy and the bandgap is demonstrated. Results of these band structure can be used as a guide for the design and the selection of the optimum strain and crystal orientation configuration of uniaxial strained silicon devices.