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

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... arison to the thermal energy. The difference between R_K and R_D decreases with the dimensionless damping parameter ϕ, however, does not become smaller than 10-20 unexpected growth of the difference between R_K and R_D with the governing parameter is observed.