This paper examines the application of neural networks to the partitioning of unstructured adaptive meshes for parallel explicit time-stepping finite element analysis. The use of the mean field annealing (MFA) technique, which is based on the mean field theory (MFT), for finding approximate solutions to the partitioning of the finite element meshes is investigated. The partitioning is based on the recursive bisection approach. The method of mapping the mesh bisection problem onto the neural network, the solution quality and the convergence times are presented. All computational studies were carried out using a single T800 transputer.