  We investigate the magnetic interactions in triangular rare-earth
delafossites materials NaYbO$_2$ and NaYbS$_2$ via first-principles
calculations. The calculated Curie-Weiss temperatures are in good agreement
with experiments. We perform classical Monte Carlo simulations of the two
compounds using the extracted exchange parameters. We find that if only the
nearest neighbor interactions are considered, the magnetic ground states of
NaYbO$_2$ and NaYbS$_2$ are a stripe and a planar 120\degree~ N\'{e}el state,
respectively. The simulated transition temperatures are much higher than the
lowest experimental temperatures, where no magnetic ordering was observed.
However, we show by adding suitable second neighbor interactions, the {\it
classical} magnetic ground state of NaYbO$_2$ becomes to the $Z_2$ vortex
phase, and the simulated specific heat $C_v$ are very similar to the
experimental observations, with no obvious phase transition down to the
extremely low temperature.
