Quasi tetrahedral agglomerates consist of four primary particles, from which three primary particles generally form a base area on which the fourth primary particle is arranged centrally; in the regular case the primary particles having equal radii. The coordinates of the centers of the primary particles are derived for agglomerates exhibiting equal primary particles (regular tetrahedron) and primary particles of different radii (inclined tetrahedron). Moreover, an analytical model for elastic contact deformation is derived on the basis of the Hertz model. Subsequently, tetrahedral agglomerates are modeled using the discrete element method and the compression test between two rigid plates is simulated and compared with experimental results.