The PROTO-SPHERA experiment (under construction in Frascati inside the START vacuum vessel) aims to study the properties of a spherical torus (ST), where a hydrogen force-free screw pinch (SP, with open field lines and fed by electrodes) replaces the central rod of the standard spherical tokamak experiments: PROTO-SPHERA, with a central screw pinch current Ie = 60 kA, aims at producing a spherical torus (with closed field lines) of diameter 2Rsph = 70 cm, and aspect ratio R/a = A = 1.2–1.3, carrying a toroidal current Ip = 120–240 kA. Such a configuration is an evolution of the flux core spheromak (FCS) concept, first proposed by Taylor. The formation mechanism of the configuration will be the one successfully developed by the TS-3 team at the University of Tokyo. The spherical torus toroidal current should be sustained by helicity injection from the screw pinch, therefore some level of resistive instability with toroidal mode numbers n = 1 and/or n = 2 is requested after the formation and during the sustainment phase; nevertheless, the configuration should be operated such as to maintain it stable from an ideal MHD point of view. The ideal MHD stability limits of PROTO-SPHERA have been analysed by a numerical code able to handle magnetic configurations endowed with both closed and open magnetic field lines. The results of such an analysis are presented in terms of the main parameter, which is the ratio between the currents in the spherical torus and in the central screw pinch, Ip/Ie, and of other relevant parameters of the ST (elongation, aspect ratio, total beta and the toroidal plasma current profile). A comparison with the TS-3 results is also shown.