The framework of this paper is the parallelization of a plasticity algorithm that uses an implicit method and an incremental approach. More precisely, we will focus on some specific parallel sparse linear algebra algorithms which are the most time-consuming steps to solve efficiently such an engineering application. First, we present a general algorithm which computes an efficient static scheduling of block computations for parallel sparse linear factorization. The associated solver, based on a supernodal fan-in approach, is fully driven by this scheduling. Second we describe a scalable parallel assembly algorithm based on a distribution of elements induced by the previous distribution for the blocks of the sparse matrix. We give an overview of these algorithms and present performance results on an IBM SP2 for a collection of grid and irregular problems.