Stochastic lattice structures are modeled using a generative algorithm. In particular, the voronoi tessellation technique is applied for modeling cellular solids with irregular cell geometry and variable strut sections. The ligaments are formed considering the volume and shape characteristics of the voronoi cells. This way, the strut cross section variability is linked to the adjacent cell topology. The developed geometry is used for 3D printing the structures through a high accuracy SLA 3D printer. The mechanical properties of the photosensitive resin were determined by conducting tension experiments on appropriate 3D printed specimens. The printed stochastic structures were subjected to compressive loads in order to investigate their mechanical response. A finite element model of the compressive tests using the generated geometry, is also developed. The calculated results provide a good correlation with the experimental ones and also provide precious insight for the characterization of the mechanical behavior of the tested structures.