The study of the Poisson’s ratio constitutes a crucial aspect of materials science, as it is directly related to the deformation behavior of a material when subjected to stress. The investigation of Poisson's ratio in cellular solids holds immense significance, especially in the context of mechanical applications. Understanding their Poisson's ratio deepens the knowledge of their deformation properties and paves the way for revolutionary advancements in various engineering applications. This investigation focuses explicitly on examining the Poisson’s ratio of two types of cellular solids, namely, hexagonal and re-entrant honeycomb structures. The latter is a unique cellular material with a negative Poisson’s ratio and is commonly referred to as an auxetic structure. In this study, we explore how changes in the microstructure of the cellular solids, including modifications in the cell wall thickness and angle, affect the Poisson’s ratio. This study revealed a strong dependency of the Poisson’s ratio on the microstructure of the cellular solids, with the re-entrant honeycomb structure exhibiting a negative Poisson’s ratio than the hexagonal structure. By shedding light on Poisson's ratio behavior of these cellular structures, we can provide valuable insights that have important implications for developing novel lightweight materials, particularly in aerospace applications, where high strength and low weight are critical.