The microstructure and properties of suspensions of nonspherical particles are influenced by the specific particle shapes through hydrodynamic interactions, but here traditional numerical approaches of solving the Stokes equations are limited to small systems by computational cost, and often to special particle arrangements by symmetry requirements. On the other hand, the analytical development of a hydrodynamic mobility algorithm for Stokesian dynamics (SD) simulations of rigid nonspherical particles is mathematically involved, must be derived for each distinct particle shape needed, and cannot handle deformable particles. Hence we present algorithms for SD simulations of arbitrary shape particles, rigid or flexible, constructed with appropriate constraints among rigid spherical particles whose hydrodynamic mobility is computable by various available schemes, including ours [J. Chem. Phys. 112, 2548 (2000)]. The optimal algorithm also provides for rigid attachment among particles during simulation, by aggregation for example. Its implementation for a system with internal coordinate constraints is tested in simulations of aggregation of spheres and sedimentation of spheroids and chains in bounded and unbounded geometries. (C) 2003 American Institute of Physics.