CUDAHM accelerates Bayesian inference of Hierarchical Models using Markov Chain Monte Carlo by constructing a Metropolis-within-Gibbs MCMC sampler for a three-level hierarchical model, requiring the user to supply only a minimimal amount of CUDA code. CUDAHM assumes that a set of measurements are available for a sample of objects, and that these measurements are related to an unobserved set of characteristics for each object. For example, the measurements could be the spectral energy distributions of a sample of galaxies, and the unknown characteristics could be the physical quantities of the galaxies, such as mass, distance, or age. The measured spectral energy distributions depend on the unknown physical quantities, which enables one to derive their values from the measurements. The characteristics are also assumed to be independently and identically sampled from a parent population with unknown parameters (e.g., a Normal distribution with unknown mean and variance). CUDAHM enables one to simultaneously sample the values of the characteristics and the parameters of their parent population from their joint posterior probability distribution.