This work presents a full plastic formulation to be applied within topology optimization. The main idea of topology optimization in solid mechanics is to find the material distribution within the domain so that it optimizes a performance measure and satisfies a set of constraints. One might seek to minimize the compliance satisfying that the volume is less than a given value. The aforementioned formulation is the standard topology optimization which has been used widely in literature. Although it provides interesting results, additional requirements must be taken into account when practical application is concerned. Structures are designed considering two main aspects: (i) the structure must not collapse, supporting the applied loads (safety criterion); and (ii) its displacements must be lower than a prescribed bound (serviceability criterion). Consequently, the standard formulation shall be modified, finding the material distribution corresponding to the minimum volume such that the safety criterion is met. Said safety criterion may be defined as restraining the elastic stresses to the yield criterion in the entire domain. This definition has resulted in a new branch in this research field: the stress constrained topology optimization. On the other hand, it is understood that the plastic design criterion is preferable when optimization is intended, since it fully exploits the material strength. Therefore, this work addresses the incorporation of the plastic design criterion into topology optimization as a more advantageous method than standard and stress constrained topology optimization methods. The proposed formulation is an extension of limit analysis, which provides an estimative of the collapse load of a structure directly through mathematical programming, ensuring computational efficiency to the proposed methodology. Lastly, numerical examples are shown to verify plastic topology optimization and the final topology is compared with those provided by standard and stress constrained topology optimization methods.