Based on progressively Type-II censored samples, this pape r deals with inference for the stress- strength reliability R = P ( Y < X ) when X and Y are two independent Weibull distributions with different scale parameters, but having the same shape param eter. The maximum likelihood esti- mator, and the approximate maximum likelihood estimator of R are obtained. Different confidence intervals are presented. The Bayes estimator of R and the corresponding credible interval using the Gibbs sampling technique are also proposed. Further, we consider the estimation of R when the same shape parameter is known. The results for exponenti al and Rayleigh distributions can be obtained as special cases with different scale parameter s. Analysis of a real data set as well a Monte Carlo simulation have been presented for illustrativ e purposes.