Starting from the Keating model, a semi-continuum atomistic lattice model, with directly taking into account the discrete nature in width and thickness direction, is proposed to calculate the elastic constants and Youngs modulus of single crystal silicon nanowires (SiNWs). Based on the six-band k·p theory and the deformation potential concept, and taking into account the quantum-size effect and spin-orbit coupling, a numerical model for the valence band structures of SiNWs in various transport orientations is established by using the finite difference method. Then we use a top-of-the-barrier ballistic field-effect transistor (FET) model to investigate the effects of the uniaxial stress and the elastic constants on ballistic transport properties of the p-type SiNW FETs in combination with the calculation results from the two models mentioned above. It is found that the elastic constants and Youngs modulus of the SiNW are highly size-dependent, which is in good agreement with the available molecular dynamics result. Furthermore, our calculations indicate that the effect of size-dependent elastic constants on ballistic transport current of the SiNW FET strongly depends on the effect of the uniaxial stress on ballistic transport current, because when the uniaxial stress induces a significant change in valence band structures of SiNWs, the size-dependent elastic constants can obviously modify the valence band structure.