The analytical expressions of the far-field divergence angle,the beam width and the M2-factor in rectangular coordinate systems for laser beams propagating in atmospheric turbulence are derived by using the extended Huygens-Fresnel principle and the definition of the second moments of the Wigner distribution function. Taking the elegant Hermite-Gaussian (EHG) beams as typical examples of laser beams,the propagation properties of the EHG beams in turbulence are analyzed quantitatively. It can be shown that the M2-factor of the laser beams in atmospheric turbulence is related to the M2-factor of the incident plane,the second moments of the incident plane,the propagation distance in turbulence,wavenumber and the influence factor of the atmospheric turbulence. Specially,the far-field divergence angle,the beam width and the M2-factor of the EHG beams increase with the propagation distance in turbulence. And the influences of the atmospheric turbulence on the far-field divergence angle angle,the beam width and the M2-factor of the EHG beams with higher beam order are smaller. The M2-factor of the EHG beams depends on the propagation distance,the structural constant of the refractive index fluctuations of the turbulence,the wavelength,the beam order and the waist width of the fundamental-mode Gaussian beam.