A LIBS system is demonstrated using a 100m cavity Yb fiber oscillator producing ~ 70ps, 320nj clusters of 50-100fs sub-pulses at 2MHz. A new empirical model for femtosecond ablation is presented to explain the LIBS signal intensity’s non-linear dependence on pulse fluence by accounting for the Gaussian beam’s spatial distribution. This model is compared to experimental data and found to be superior to linear threshold fits. This model is then used to measure the ablation threshold of Cu using a typical amplified Ti:Sapphire system, and found to reproduce previously reported values to within ~ 20%. The ablation threshold of Cu using the Yb fiber oscillator system was measured to be five times lower than on the amplified Ti:Sapphire system. This effect is attributed to the formation of nanostructures on the surface, which have previously been shown to decrease the ablation threshold. The plasma lifetime is found to be ~ 1ns, much shorter than that of nanosecond ablation, further indicating that the decreased threshold results from surface effects rather than laser-plasma interaction. The low threshold and high pulse energy of the Yb fiber oscillator allows the acquisition of LIBS spectra at megahertz repetition rates. This system could potentially be developed into a compact, fiber-based portable LIBS device taking advantage of the benefits of ultrafast pulses and high repetition rates.