Oscillations of a flexible pipeline with flowing liquid are considered taking into account the periodic internal pressure caused by equipment discharge (pumps, compressors). The problem of the optimal control of the object by the criterion of resources minimum with additional restrictions on the value and speed of the control (inertial control) is solved. The numerical method of reduction to unconditional minimization for calculation of switching moments of piece-linear on/off control is presented. Numerical examples of oscillation damping at different number of control stages and different initial conditions are demonstrated.