Abstract: Porous structures, owing to their excellent characteristics, are widely used in aerospace, biomedical, and various engineering applications. Hollow columns, due to their unique structure, are extensively employed to bear structural loads. Therefore, the study of the axisymmetric contact problem between hollow columns and porous half space is particularly important. In this paper, the Hankel transform is used to transform the contact problem into the problem of solving an integral equation, and exact expressions for surface contact stress and displacement are derived. The Gauss-Chebyshev method coupled with the infinite integration of product-type Bessel functions for solving integral equations is developed, and degradation comparisons are carried out to verify the correctness of the method. The results indicate that the method has better computational accuracy and performance at singular points. The numerical results show the variations of surface contact stress with respect to Poisson's ratio, porosity, mechanical loading, inner diameter, wall thickness (hollow cylinder), and radius (bowl shaped parabolic column). The study additionally provides insights into the displacement variation concerning porosity, inner diameter, wall thickness, radius, and depth. The results further indicate that the center of the contact region of the substrate has obvious superimposed deformation, and the singularity of the outer side of the contact region is higher than that of the inner side. Therefore, it is more likely that the outer side is the initial position for cracks. Furthermore, for a smaller inner diameter, when the wall thickness of the hollow column matches the radius of the solid column, the stress singularity at the outer edge of the contact area of the substrate caused by the hollow column is more than 1 times smaller compared to that caused by the solid column, and this ratio decreases as the porosity increases. On the other hand, when the outer diameter of the hollow column matches the radius of the solid column, the stress singularity at the outer edge of the contact area of the substrate caused by the hollow column is more than 1 times larger compared to that caused by the solid column, and this ratio increases with an increase in the porosity. The research results have important guiding significance in the design and application of porous materials.