We present Bayes estimators for the parameters of Burr type XII distribution under the symmetric squared error loss function and the asymmetric linear exponential loss function based on a simple prior distribution. In all cases the estimator turns out to be ratios of integrals. We present approximate Bayes estimators based on different approximation techniques. We demonstrate the application of Burr type XII distribution to model the time to death in a clinical trial of carcinoma patients comparing two therapies.