We study tail properties of the distribution of the supremum within finite time horizon of L'evy process with negative drift. We consider the case where the jumps of the process are subexponentialy distributed. The asymptotics obtained are uniform in time horizon. We show what is similar to the case of a random walk and discuss differences. Also we study similar problem for the compound renewal process and specify these results for the compound Poisson process. Applications are given to the Cram'er-Lundberg risk model.