Based on the methods of vector angular spectrum and stationary phase, the analytical expressions of the transverse electric (TE) and transverse magnetic (TM) terms and energy flux distributions of two edge dislocations in Gaussian beams in the far field are derived and used to analyze the phase singularities and energy flux distributions. The result shows that two edge dislocations appear in the electric field component on condition that two off-axis distances are equal to zero. The edge dislocations will vanish and optical vortices may take place when two off-axis distances are nonzero. Edge dislocations and optical vortices and energy flux distributions are symmetric about the origin. With increasing the off-axis distances, optical vortices and black nuclei in the energy flux distributions move toward the origin and coincide at the origin.