Abstract A neural network approach is proposed for the effective numerical treatment of the analysis problem of above-ground pipelines on unilateral supports. As is well known, the structural response of such pipelines can be effectively described by monotone problems having the form of quadratic minimization problems with inequality constraints. In order to numerically treat these quadratic problems, the methods of the theory of neural networks are applied. Within such a neural network computing framework, the Hopfield model is first appropriately generalized, and then a neural network model covering the case of inequalities is proposed. A numerical application illustrates the proposed neural network method.