The paper focuses on experimental measurement and analytical and numerical modeling of the elastic moduli of porous Si3N4 ceramics obtained by 3D printing and pressureless sintering. The pores in such a material have complex irregular shape and porosity varies over a wide range (up to 50%), depending on the technological parameters used. For analytical modeling, we use effective field methods (Mori-Tanaka-Benveniste and Maxwell homogenization schemes) recently developed for pores of superspherical shape. For FEM simulation, we used microstructures generated by overlapping solid spheres and overlapping spherical pores. It is shown that elastic properties of ceramics are largely determined by the granular structure and the concave pore shape, which have been observed in the ceramics microstructure after sintering of the 3D-printed powder green bodies.