Graphics processing units (GPUs) are rapidly emerging as a more economical and highly competitive alternative to CPU-based parallel computing. As the degree of software control of GPUs has increased, many researchers have explored their use in non-gaming applications. Recent studies have shown that GPUs consistently outperform their best corresponding CPU-based parallel computing alternatives in single-instruction multiple-data (SIMD) strategies. This study explores the use of GPUs for uncertainty quantification in computational mechanics. Five types of analysis procedures that are frequently utilized for uncertainty quantification of mechanical and dynamical systems have been considered and their GPU implementations have been developed. The numerical examples presented in this study show that considerable gains in computational efficiency can be obtained for these procedures. It is expected that the GPU implementations presented in this study will serve as initial bases for further developments in the use of GPUs in the field of uncertainty quantification and will (i) aid the understanding of the performance constraints on the relevant GPU kernels and (ii) provide some guidance regarding the computational and the data structures to be utilized in these novel GPU implementations.