Abstract This study deals with optimal design of cantilevered fluid-conveying pipes. The aim is to maximize the critical flow speed of the fluid by means of additional masses, supporting springs or dampers along the length of the pipe. The optimization problem was formulated by modelling the pipe by FEM, using Euler-Bernoulli beam elements. The locations of the additional masses, springs and dampers and the properties of these elements (mass, spring constant and damping constant) were chosen as design parameters. The maximization problem for the critical fluid flow speed was solved by the sequential quadratic programming (SQP) technique. In addition to the presentation of the optimal values obtained for the design parameters, some aspects of the sensitiveness of the systems to variations in these parameters and the robustness of the optimum designs with respect to the stability of the system are studied. Although a considerable increase in the critical flow velocity of the fluid can be achieved in the example cases studied here, a marked sensitivity of the system to the location and properties of the additional elements in the optimum designs was observed. Also, the margin with respect to stability seems to be relatively small in some of the optimum designs considered. Non-linear numerical analysis confirmed the findings of the linear analysis with respect to the sensitivity of the optimum designs to the properties of the additional elements and revealed a very rich post-critical dynamic behaviour in the optimized structures.