A systematic geometric algorithm is developed to generate particle packing with high density, controllable gradation, and uniform spatial distribution for discontinuous deformation analysis (DDA). The algorithm incorporates a lattice searching technique to expedite overlap detection and reduce computational costs during particle packing generation. Additionally, a Fourier transformation method is utilized to analytically handle overlap detections on arbitrary irregular boundaries. To evaluate the efficiency and accuracy of the proposed method, a series of comparisons are made between existing methods and the proposed approach. Numerical modelling of engineering problems is conducted using the proposed method and a self-developed numerical program called DDA. The modelling results demonstrate that the proposed particle generation method has wide applications in generating complex particle models for discontinuous numerical analysis. The algorithm exhibits excellent performance in both geometric and numerical analyses, further confirming its efficiency and accuracy. Article Highlights A systematic geometric algorithm is developed to generate particle packing with controllable internal characteristics. The algorithm integrates a lattice searching algorithm to expedite particle generation. The algorithm incorporates the Fourier transformation method to handle overlap detections on arbitrary irregular boundaries.