Nowadays high-throughput technologies are generating many types of high-dimensional data such as genomic and proteomic data and meta-data in survival analysis. One of the needs of analysis with such failure time data with very high-dimensional covariates is to obtain a system-level understanding of various complex diseases. An important recent area of application is microarray data analysis, i.e. investigating the relationship between a censored survival outcome and microarray gene expression profiles. Because of the small sample size and large number of covariates in such situations, frequentist methods for the variable selection process can be unstable and result in over-fitting. This research focuses instead on the Bayesian approach to identifying the most influential covariates (predictors) when fitting parametric accelerated failure time (AFT) models. The performance and sensitivity of such Bayesian variable selection methods will be analysed and demonstrated using both simulated and real datasets. This study concentrates on the AFT model since it has an intuitive physical interpretation and is a useful alternative to the more popular Cox proportional hazards model.