Based on the generalized Huygens-Fresnel integral and the second-order moments of the Wigner distribution function,the analytical formulas for the root-mean-square (rms) spatial width,rms angular width and M²-factor of electromagnetic Gaussi an-Shell model array beams (EGSMA beams) propagating through the atmospheric turbulence are derived.The relationships of the propagation properties of EGSMA beams in turbulence with the initial beam wi dth,initial coherence length,the beam array number,initial degree of polarization,inner scale of t he turbulence and the structure parameter of the refractive index fluctuations of the turbulence are a nalyzed.The results show that compared with the relative M²-factor decreases with the decreases of initial deg ree of polarization,coherence lengths and the refractive index fluctuations of t he turbulence,and with the increases of beam array numbe r,larger beam width and larger inner scale,the relative M²-factor of EGSMA be ams in turbulence is less affected by turbulence.And it is known that when the propagation distance is about 5km or m ore,the influence of coherence lengths on the relative M²-factor is increa sed obviously as the increase of propagation distance. Furthermore,it is also found that the value of the relative M²-factor is close to 1with the beam array number increasing.Meanwhile,the relative M²-factor is influenced by the structure parameter of the refractive index fluctuations of the turbulence more seriously compared with tho se influenced by the relative rms spatial width and angular width.