The foundation of a lunar habitation may be either smooth or rough with different shapes in the light that various concepts of the lunar base have been proposed, which require a good understanding of the bearing behavior of the lunar soil under plates with different shapes and roughness. Therefore, the three-dimensional distinct element method (3D DEM) is employed here to perform plate load tests on lunar soil simulant using the force-driven method. The soil failure mechanism under different plates is first described at various scales with detailed DEM studies of the load-settlement curve, stress path, ground heave, void ratio changes, and normalized-velocity field. Following these, the shape factor and coefficient of plate roughness are discussed by comparing the DEM and theoretical results. The results show that a typical general failure model can be identified for the strip plate, a local failure model for the circular and square plates, and a Hill model for the smooth plate from the ground heave, void ratio changes, and normalized velocity field. The shape factors for bearing capacity determined by the settlement criterion are close to those by the Terzaghi method with an error of nearly 10%, and the shape factors for the deformation modulus are similar to those in Chinese standard with an error of nearly 20%. In addition, the coefficient of plate roughness for the semi-rough plate is close to those predicted by the Meyerhof and Kumar methods with an error of nearly 5%.