In this paper, we discuss the estimation of location and scale parameters of the Rayleigh distribution based on the Upper record values by the best linear unbiased estimator (BLUE) and an alternative linear estimate, proposed by Gupta (1952). Type II singly and doubly censored samples are used for estimation. Tables of coefficients for best linear estimator and alternative estimator of are presented for various choices of censoring for n 8. Variances and covarinces of estimator of for BLUE and for alternative estimator are also presented. The computational formula and procedure used are explained. The purpose of the paper is to compare the performance of the estimation procedures in terms of relative efficiencies. The findings of the study suggest that the BLUE method can be replaced by Gupta method especially in the large samples.