This paper describes a parallel processing implementation for neural computing and its application to finite element mesh decomposition. The parallelized neural network software developed is based on the public domain NASA developed program NETS 2.01, which is based on the back propagation algorithm of Rumelhart et al. [Learning internal representation by error propagation. In: Parallel Distributed Processing: Explorations in the Microstructure of Cognition (Edited by D. E. Rummelhart and J. L. McClelland), Vol. 1: Foundations. MIT Press, MA (1986)]. The principal focus of this research concerns the parallel implementation. Comparisons between sequential and parallel versions are given. Finally a structural design problem concerned with finite element mesh generation is solved using the parallel neural network software.