Slowly growing magnetohydrodynamic (MHD) instabilities are usually detected experimentally in supershot plasmas in the Tokamak Fusion Test Reactor [in Plasma Physics and Controlled Nuclear Fusion Research 1986, Kyoto (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 75] (TFTR). These instabilities, when they occur, result in deterioration of the confinement and limit the attainable beta. Using initial profile data from transport analysis of specific high beta supershot plasmas, the predictions of the single fluid, linear MHD stability model are studied and compared with the experimental observations. It is shown that, in the highest beta plasmas achieved, the pressure gradients in the interior are such that the absence of the 1/1 mode is difficult to reconcile with the single fluid MHD model if the safety factor, q < 1. On the assumption that q exceeds unity everywhere, it is found that supershot plasmas are predicted to be unstable or near marginal to small toroidal mode number, pressure-driven instabilities of the ballooning variety. When finite plasma resistivity is included in the analysis the range of parameters over which these instabilities are excited is significantly extended.