The initial stage of solid phase epitaxial (SPE) growth of GaAs films on the vicinal Si (001) substrate was investigated by high resolution transmission electron microscopy (H-RTEM). Cross-sectional  and  HRTEM images show that the SPE growth of crystalline GaAs islands from the amorphous phase proceeds via the formation of three-dimensional islands at the initial stage and islands' size and spacing are not critically dependent on the substrate tilt direction. The average vertical and lateral dimensions of islands were found to be 9 nm and 14 nm respectively, and the average island spacing was 10 nm. Moreover, many internal stacking faults (and/or microtwins) and a few dislocations have been already formed at this initial stage of growth. In addition, the critical thickness for misfit dislocation formation is found to depend upon the islands' lateral dimensions as well as the heights.