Compute Unified Device Architecture (CUDA) is a software platform for massively parallel high-performance computing on NVIDIA GPUs. This package provides a CUDA implementation of a Bayesian multilevel model for the analysis of brain fMRI data. A fMRI data set consists of time series of volume data in 4D space. Typically, volumes are collected as slices of 64 x 64 voxels. Analysis of fMRI data often relies on fitting linear regression models at each voxel of the brain. The volume of the data to be processed, and the type of statistical analysis to perform in fMRI analysis, call for high-performance computing strategies. In this package, the CUDA programming model uses a separate thread for fitting a linear regression model at each voxel in parallel. The global statistical model implements a Gibbs Sampler for hierarchical linear models with a normal prior. This model has been proposed by Rossi, Allenby and McCulloch in `Bayesian Statistics and Marketing', Chapter 3, and is referred to as `rhierLinearModel' in the R-package bayesm. A notebook equipped with a NVIDIA `GeForce 8400M GS' card having Compute Capability 1.1 has been used in the tests. The data sets used in the package's examples are available in the separate package cudaBayesregData.