Abstract: The discrete element method (DEM) is a powerful tool to study the microscopic mechanics behind the complicated macroscopic mechanical behaviors of clay. In the current DEM simulations of clay, the planar shape of clay platelets is commonly assumed to be regular, such as rectangle and ellipse, which are quite different from the true planar shapes of clay. There is no research report about the effects of shape of clay platelets on the mechanical behaviors of clay. In this study, the methods to calculate the Van der Waals force and the double-layer repulsive force between two convex-shaped clay platelets are proposed, and an inter-clay platelet contact model is developed. Then, the effects of relative alignment of two clay platelets on the interactions are studied, and the approaches to significantly improve the simulation efficiency are summarized accordingly. The DEM simulation for clay based on irregular convex planar shape of clay platelets is thus developed. The simulated results indicate that the developed DEM simulation scheme can well reproduce the mechanical behaviors of clay in oedometer tests. The planar shape and thickness of clay platelets have significant effects on the one-dimensional compressive curves and the evolution of platelet arrangement fabric. It is necessary to incorporate the irregular planar shape of clay platelets in future DEM simulation of clay.