Light propagation in disordered media is a fundamental and important problem in optics and photonics. In particular, engineering light-matter interaction in disordered cold atomic ensembles is one of the central topics in modern quantum and atomic optics. The collective response of dense atomic gases under light excitation, which crucially depends on the spatial distribution of atoms and the geometry of the ensemble, has important impacts on quantum technologies like quantum sensors, atomic clocks and quantum information storage.Here we analyze near-resonant light transmission in two-dimensional dense ultracold atomic ensembles with short-range positional correlations. Based on the coupled-dipole simulations under different atom number densities and correlation lengths, we show that the collective effects are strongly influenced by those positional correlations, manifested as significant shifts and broadening or narrowing of transmission resonance lines. The results show that mean-field theories like Lorentz-Lorenz relation are not capable of describing such collective effects. We further investigate the statistical distribution of eigenstates, which are significantly affected by the interplay between dipole-dipole interactions and position correlations. This work can provide profound implications on collective and cooperative effects in cold atomic ensembles as well as the study of mesoscopic physics concerning light transport in strongly scattering disordered media. simplest hard-sphere-type correlation which exists in densely packed hard spheres [32] can usually increase the transport mean free path of light [33,34]. Screened Coulomb potential induced positional correlations in nanoparticle colloidal suspensions were found to induce strongly negative asymmetry factor [35,36]. Recently, some unexpected optical properties like optical transparency [37], enhanced absorption [38] and isotropic photonic band gaps [39][40][41][42] were discovered in 2D and 3D disordered media with certain structural correlations, e.g., the stealthy hyperuniform media. Therefore, structural correlations offer a great opportunity for tailoring the optical properties of disordered materials, with promising applications like structural coloration [43,44], bright white paints [45] and solar energy harvesting [38,[46][47][48][49], etc.Despite these fascinating advancements, however, it is still not fully understood how structural correlations affect optical properties of disordered media, even for an ideally simple system composed of randomly distributed spherical scatterers [45,[50][51][52][53]. In particular, the interplay between structural correlations and near-field as well as far-field electromagnetic interactions among scatterers is still not very clear [50,51,54], especially near single scatterer internal resonances (like Mie resonances for dielectric nanoparticles) at high packing density [55][56][57][58][59].On the other hand, the last three decades have witnessed the rapid development of laser cooling and trapping of atoms to r...