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The axial vibration of the liquid-filled pipes can be represented with a four-equation fluid–structure interaction (FSI) model. When distributed friction was neglected, this model could be solved with an exact solution without computational grid, while the only weakness was the high time cost. A fast meshless solution (FMS) developed earlier used the time-line interpolation rather than the recursive algorithm, to speed the calculation. For the purpose of practical applications, the FMS for supports at pipe end and middle position is proposed, and series connection is also studied in this paper. The support is described by the complex constraint including elastic, damping and inertial effects. A numerical case of the double-pipe water hammer is employed to validate the series connection and end supports. The FMS for the middle support is validated by an existing experiment, where the support can be described by the dry friction. Both numerical and experimental cases indicate the effectiveness and the efficiency of the proposed solution method. • The fast meshless solution for the double pipe is proposed. • Complex constraints at pipe supports are incorporated and solved. • Calculation efficiency is improved significantly and high accuracy is achieved. [ABSTRACT FROM AUTHOR]