An epithermal facility for treating patients with brain gliomas has been designed and is under construction at the fast reactor TAPIRO at ENEA Casaccia (Italy). The calculational design tools employed were the Monte Carlo codes MCNP/MCNPX together with the DSA in-house variance reduction patch. A realistic anthropomorphic phantom ("ADAM") was included to optimise dose profiles and in-phantom treatment-planning figures-of-merit. The adopted approach was to minimise the treatment time whilst maintaining a reasonable therapeutic ratio. It is shown that TAPIRO, in spite of its low power of 5 kW, is able to provide an epithermal beam that is of good quality and of sufficient intensity to allow a single beam patient irradiation, under conservative assumptions, of 50 min.