The article considers a two-dimensional formulation of the problem of hydrodynamic atmospheric escape by example of the warm mini-Neptune TOI-421c. The calculations use a spherical grid with interpolation of the EUV intensity function from a rectangular grid. The obtained two-dimensional profiles of physical parameters in the upper atmosphere are presented. It is shown that calculations in a one-dimensional formulation of the problem overestimate the mass-loss rate, and a fitting parameter has been established to refine this rate. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.