The authors discuss the parallelization of a plasticity algorithm which is based on an implicit method and an incremental approach. Parallel sparse block factorization methods for solving the corresponding large systems of linear algebraic equations in each linearization step and the parallel assembly of the system matrices are discussed and analyzed. Especially, an algorithm which computes an efficient static scheduling of block computations for the parallel sparse factorization technique is proposed. The presented numerical experiments show a good scalability of the proposed algorithms.