Irregular honeycomb structures occur abundantly in nature and in man-made products, and are an active area of research. In this paper, according to the optimization of regular honeycomb structures, two types of irregular honeycomb structures with both positive and negative Poisson’s ratios are presented. The elastic properties of irregular honeycombs with varying structure angles were investigated through a combination of material mechanics and structural mechanics methods, in which the axial deformation of the rods was considered. The numerical results show that axial deformation has a significant influence on the elastic properties of irregular honeycomb structures. The elastic properties of the structure can be considered by the enclosed area of the unit structure, the shape of the unit structure, and the elastic properties of the original materials. The elastic properties considering the axial deformation of rods studied in this study can provide a reference for other scholars.