Irregular polygon shapes (eg, with small edges or small angles) are usually encountered in the contact simulation of discrete block systems. Treatment of irregular polygons in contact detection process has critical effects on the robustness and efficiency of the discontinuous computation approach. The present work proposes a cover-based strategy to detect and solve contacts of irregular convex polygons in a robust and efficient way. Contact constraints of two polygons are represented by vertex-edge and edge-vertex contact covers in 2D. Two loops, namely vertex-edge loop and edge-vertex loop, and two filter criteria, namely the entrance filter criterion and the distance filter criterion, are used to establish the potential contact cover list of two neighbor polygons. The initial active and closed contact covers are chosen based on block configuration at the beginning of the step and they are then updated in the open-close iteration process using proposed criteria. This strategy is implemented in discontinuous deformation analysis. The robustness of the proposed cover-based approach and the conventional type-based approach in handling contact of irregular blocks is verified first. Then, the contact analysis efficiency of the cover-based approach with different contact tolerances is evaluated. This cover-based method can be extended to 3D case for efficient and robust contact analysis of irregular polyhedral blocks. © 2020 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd