P-CORONA models the intensity and polarization of coronal atomic lines in any given three dimensional (3D) model of the solar corona. It takes into account the scattering of anisotropic radiation as well as the symmetry-breaking effects arising from the influence of magnetic fields, through the Hanle and Zeeman effects, and from non-radial solar wind velocities. The code solves the statistical equilibrium equations for the elements of the atomic density matrix corresponding to the multi-level atomic model under consideration, assuming complete frequency redistribution. The calculations are carried out assuming an optically thin plasma, with the emergent Stokes profiles resulting from the integration of the local emission coefficients along the line-of-sight in the chosen 3D coronal model. P-CORONA incorporates HDF5 input/output functionality and includes a graphical user interface.