The fluid-elastic instability is probably to occur in both transverse and streamwise directions. The studies of streamwise instability are mainly performed with the tubes are fixed in the transverse direction, which may not happen in the practical tube bundles. In this study, the effect of asymmetry of the tube stiffness on the streamwise instability was investigated through water tunnel tests and numerical simulations. The vibration was controlled by changing the stuffiness of tubes in the two directions. The results show that the streamwise vibration can affect instability threshold in the transverse direction in single tube tests, and the streamwise vibration was suppressed when the tubes fall into instability in transverse direction. The asymmetry of the tube stiffness can have an effect on streamwise and transverse instability, but the effect is not pronounced in the multi-flexible tube array.