This paper presents new algorithms for the generation of three-dimensional (3D) solid particles. It considers the randomness in shape. First, it presents an algorithm to generate a polyhedron, considering convexity and concavity. Novel controlling parameters are presented. Second, it introduces two parameters to evaluate the particle's shape. Sphericity (S-p) and Angularity Index (AI) quantify the overall and local shape properties. Finally, this paper discusses the effects of the controlling parameters on the shape characteristics. Results show the controlling parameters can determine the shape of a particle precisely. However, Al is more complex compared with Sr for a specific particle's shape. It is hard to obtain the corresponding controlling parameters (N-mid and Delta) for the particle with specified AI. The algorithms presented in this paper have potential applications in such areas as granular, powder, multiphase fluid dynamics and other particulate systems. (C) 2016 Elsevier B.V. All rights reserved.