The purpose of this study is to investigate the physical property of catheter, which is made of soft nylon resin and reinforced with thin stainless wires. The buckling behavior under initial torsion has been examined by using short length specimens, and the effect of stress relaxation on the buckling behavior has been revealed in the previous report. However, the snap-through phenomenon occurs when using relatively long specimens. So, in this report, the buckling tests under the combined loading for torsion and compression are conducted with various longitudinal lengths of specimens by changing the speeds of axial displacement and the angle of twist. Especially, the conditions that the snap-through behavior occurs are investigated by performing the experiments with various axial displacement speeds and rotational speeds, and the relation between the snap-through phenomenon and the visco-elastic behavior are revealed.