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The performance of feed-forward neural networks trained with the backpropagation algorithm on a dedicated Beowulf cluster is analyzed. The concept of training set parallelism is applied. A new model for run time and speedup prediction is developed. With the model the speedup and efficiency of one iteration of the neural networks can be estimated as a function of block size and cluster size. The model is applied to three example problems representing different applications and network architectures. The estimation of the model has a higher accuracy than traditional methods for run time estimation and can be efficiently calculated. Experiments show that speedup of one iteration does not necessarily translate to a shorter training time toward a given error level. To overcome this problem a heuristic extension to training set parallelism called weight averaging is developed. The results show that training in parallel should only be done on clusters with high performance network connections or a multiprocessor machine. A rule of thumb is given for how much network performance of the cluster is needed to achieve speedup of the training time for a neural network.