The spherical pinch (SP) concept is an outgrowth of the inertial confinement model (ICF). Unlike the ICF, where instabilities, especially the Rayleigh-Taylor instability, have been studied extensively, the instability study of the spherical pinch has just begun. The Rayleigh-Taylor instability is investigated for the first time in the SP in the present work. By using the simple condition for the Rayleigh-Taylor instability ∇ p·∇ρ<0 (density and pressure gradients have opposite direction), we have qualitatively identified the regions for development of instabilities in the SP. It is found that the explosion phase (central discharge) is stable and instabilities take place in the imploding phase. However, the growth rate for the instability is not in exponential form, and the appearance of the Rayleigh-Taylor instability does not prevent the main shock wave from converging to the center of the sphere.