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This paper presents the posibilities of adapting artificial neural networks (ANNs) to predictthe dimensionless parameters related to the maximum contact pressures of an elasticity problem. Theplane symetric double receding contact problem for a rigid stamp and two elastic strips having diferentof a rigid stamp and the lower elastic strip is bonded to a rigid support. The problem is solved under theassumptions that the contact between two elastic strips also between the rigid stamp and the uper elasticstrip are frictionless, the effect of gravity force is neglected and only compressive normal tractions can betransmitted through the interfaces. A three layered AN with backpropagation (BP) algorithm is utilizedtesting patterns are formed by using the theory of elasticity with integral transformation technique. ANpredictions and theoretical solutions are compared and seen that AN predictions are quite close to thetheoretical solutions. It is demonstrated that ANs is a suitable numerical tool and if properly used, canreduce time consumed.