MAMPOSSt (Modeling Anisotropy and Mass Profiles of Observed Spherical Systems) is a Bayesian code to perform mass/orbit modeling of spherical systems. It determines marginal parameter distributions and parameter covariances of parametrized radial distributions of dark or total matter, as well as the mass of a possible central black hole, and the radial profiles of density and velocity anisotropy of one or several tracer components, all of which are jointly fit to the discrete data in projected phase space. It is based upon the MAMPOSSt likelihood function for the distribution of individual tracers in projected phase space (projected radius and line-of-sight velocity) and the CosmoMC Markov Chain Monte Carlo code (ascl:1106.025), run in generic mode. MAMPOSSt is not based on the 6D distribution function (which would require triple integrals), but on the assumption that the local 3D velocity distribution is an (anisotropic) Gaussian (requiring only a single integral).