In epitaxial lateral overgrowth (ELOG) of III-V semiconductor on nano-trench patterned Si substrates, the most important mechanism is aspect ratio trapping, which uses high aspect ratio nano-trenches to trap threading dislocations (TDs). A model based on the theory of dislocation is proposed to calculate proportion of blocking threading dislocations in ELOG of GaAs or InP on nano-trench patterned Si substrates. The model establishes relationship with the structure of nano-trenches and the proportion of blocking threading dislocations. It is found that, the blocking proportion is determined by thickness of the masks, width of the trenches and direction of the nano-trenches (the angle of opening orientations lies off the  direction). The blocking proportion gradually increases until 100% as aspect ratio increases with fixed trench direction; with the same aspect ratio, the blocking proportion firstly decreases from 0° to 45°, and symmetrically increases from 45° to 90°. It is worth noting that the blocking proportion abruptly reduces to 50% when the direction is 45°and the aspect ratio is more than 1; But it does not happen if the aspect ratio is less than or equal to 1. The reported experimental results are well consistent with the model. The model provides a method for optimization of nano-trench patterned substrates for more effectively blocking threading dislocations in III-V semiconductors.