This paper is concerned with a numerical derivation of the sampling distributions of the Kolmogorov-Smirnov (K-S) and Cramer-Von Mises (CVM) tests for two parameter Weibull distribution using censored samples. For small and moderate sample sizes, Pearson system and Monte Carlo technique proved that the sampling distributions for the two test statistics are Pearson type II with different parameters. Tables of complete beta function can be used to obtain critical values for the two tests. Results in the case of complete samples may be considered as special cases of the present results.