  A particle in the H\'enon-Heiles potential can escape when its energy is
above the threshold value $E_{th}={1/6}$. We report a theoretical study on the
the escape rates near threshold. We derived an analytic formula for the escape
rate as a function of energy by exploring the property of chaos. We also
simulated the escaping process by following the motions of a large number of
particles. Two algorithms are employed to solve the equations of motion. One is
the Runge-Kutta-Fehlberg method, and another is a recently proposed fourth
order symplectic method. Our simulations show the escape of
H$\mathrm{\acute{e}}$non-Heiles system follows exponential laws. We extracted
the escape rates from the time dependence of particle numbers in the
H$\mathrm{\acute{e}}$non-Heiles potential. The extracted escape rates agree
with the analytic result.
