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We develop a new method of using feed-forward back-propagation (FFBP) neural networks to simultaneously estimate shape factor and depth of gravity anomalies. The advantages compared to neural network methods are the following: no pre-assumptions are made on source shape, the FFBP neural network estimates both depth and shape factor of source bodies and, once trained, works well for any new data in the training space, without repeating the initial calculations. The optimum number of neurons in the hidden layer was achieved with a novel multi-start algorithm. The FFBP model after training with suitable data sets and testing with different levels of noisy data is more robust than non-linear least squares minimization methods, especially for data with higher noise levels. The FFBP was tested for two sets of gravity field data over a major container terminal at Freeport, Grand Bahama, and a cavity anomaly at the Medford site, Florida, USA. The estimated parameters of the cavities agree well with the actual values. [ABSTRACT FROM AUTHOR]