  For the first time, the accuracy of the approximate analytical Kramers
formula for the thermal decay rate over a cusp barrier, $R_K$, is checked
numerically for the overdamping regime. The numerical quasistationary rate,
$R_D$, which is believed to be exact within the statistical errors is evaluated
by means of computer modeling of the stochastic Langevin-type dynamical
equations. The agreement between $R_K$ and $R_D$ significantly depends upon the
friction strength and the height of the barrier in comparison to the thermal
energy. The difference between $R_K$ and $R_D$ decreases with the dimensionless
damping parameter $\phi$, however, does not become smaller than 10-20%. The
unexpected growth of the difference between $R_K$ and $R_D$ with the governing
parameter is observed.
