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Simulation of flow and pressure variations in fluid pipelines using finite difference and finite element models can give unrealistic results, corresponding to errors in natural frequencies. A novel finite element model of hydraulic pipelines has been developed, using an interlacing grid system. The grid spacing is non-uniform and is optimized, using a genetic algorithm, to make some or all of the undamped natural frequencies of the model as close as possible to exact theoretical ones for a uniform pipe with the extreme boundary conditions of either constant pressure or no flow. Inaccuracies in the highest natural frequencies may be acceptable because of the effect of frequency-dependent friction and limited system frequency response. The optimized model gives accurate results in time domain simulation, and it allows variable properties and a variable integration step to be readily accommodated.