In this study of flexible piping systems (0.6 to 6.6 Hz), it was shown that the fundamental mode was not always the most significant mode of vibration. This study also concluded that variations in support condition do not significantly influence response in terms of nodal stress, fundamental frequency, and contribution of higher modes. In terms of support stiffness, the ratio of the magnitude of the gap (the total of all the mechanical tolerances and deadbands in the snubber support system) to the magnitude of the support nodal displacement was found to be more important than the actual magnitude of the gap. Additionally, when the magnitude of the nodal displacement exceeded the gap magnitude by a factor of about five or more, support stiffness was found to remain relatively constant.