An analytical solution was presented for a vertical linearly tensioned riser without flexural rigidity.In the case of less than 20 modes, natural frequencies and modal shapes of the analytical solution were in agree with those of Shear7 program. In the case of more than 20 modes, the difference of the two methods increased with mode number, so flexural rigidity could't be neglected. An equivalent vertical straight riser was defined to have approximate parameters of SCR a with catenary equation. The VIV response of the SCR was obtained through predicting the VIV response of the equivalent riser with Shear7 program. It was found that the shape of the SCR's static displacement combining with that of the equivalent riser's RMS displacement looks like a saw blade.