Selective Laser Sintered food exhibits anisotropic mechanical properties that are characteristic for its layer-by-layer manufacturing process. A constitutive model that is capable of describing the anisotropic elasto-viscoplastic-damaging behavior of the material, which was experimentally characterized by compression testing in two distinct principal orientations, is presented. Damage is modeled by applying the effective stress concept in combination with a viscoplastic flow rule that effectively regularizes damage localization. The model allows for quantitative predictions of the mechanical response of the printed food and is a valuable tool for assessing texture properties of food with Selective Laser Sintering. •The anisotropic mechanical behavior of Selective Laser Sintered food was studied.•An orthotropic constitutive model is formulated.•The effective stress concept was used for modeling anisotropic damage.•The model parameter identification was demonstrated for 3D printed food.