Unit cells are established in this paper for micromechanical analyses of particle-reinforced composites. A range of typical packing systems are examined in a systematic manner for each of them. Only the translational symmetry transformations are employed in establishing these unit cells. There are a number of important advantages resulting from this. The unit cells so derived are capable of dealing with problems involving reinforcing particles of irregular geometries and local imperfections such as debonding between the particles and the matrix, and microcracks in the matrix, provided the regularity of the packing and the orientation of the particles and the imperfections is maintained within the material. Furthermore, all the unit cells established can be subjected to arbitrary combinations of macroscopic stresses or strains using a single set of boundary conditions unlike most available unit cells in the literature, with which individual macroscopic stress or strain components may have to be analysed using different boundary conditions because of the use of reflectional symmetries. Boundary conditions for the unit cells proposed in this paper are derived from appropriate considerations of the conditions resulting from translational symmetry transformations. Applications of loads in terms of macroscopic stresses or strains and thermal loading to the unit cells are described in such a way that they can be implemented in a straightforward manner and the effective properties of composites can be evaluated following a standard and simple procedure without a numerical averaging process. The implementation of the unit cells in the micromechanical finite element analysis of particle-reinforced composites has been demonstrated fully. Spherical particles are assumed and both the particle and the matrix are assumed to be linear elastic materials and the bonding between the particle and the matrix to be perfect. 3D brick elements have been employed to generate the meshes for analysing the unit cells corresponding to various packing systems. The effective properties of the composite represented by the unit cells have been obtained through the analyses and they have been discussed and compared with results in the literature. Stress distributions in the particle and surrounding matrix have been examined. Some interesting characteristics of the different packing systems have been elaborated.