We investigate the nonlinear dynamics of high aspect ratio single wall carbon nanotubes (SWCNTs) both theoretically and experimentally. A nonlinear stretchable string model was used to describe the complicated dynamics of very slender SWCNTs with tension dominated stiffness and its transition from linear to nonlinear response. Finite difference spacial and time discretization were implemented and the resulting system of ordinary differential equations was solved numerically. A fabrication process developed to incorporate SWCNTs into patterned silicon structure was used to fabricate structures of taut, long SWCNTs suspended over trenches. Time depending electric fields were applied to the SWCNTs and their mechanical resonance responses were captured based on averaged electrical measurements (i.e., electrical resistance) of the oscillating SWCNTs. Measured resonance frequencies are reasonably consistent with those extracted from our model as resonance frequency of 24.3 MHz was measured comparing to the calculated frequency of 20.4 MHz. The transition from linear to nonlinear regime was demonstrated experimentally.