Abstarct: Instability have turned out to be the most interesting and important phenomena in physics. They arise when free energy has accumulated in a system which the system want to get rid of. In plasma physics there is a multitude of reason for the excitation of instabilities. In homogeneities may evolve both in real space and in velocity space. These in homogeneities lead to the generation of instabilities as a first linear and straightforward reaction of the plasma to such deviations from thermal equilibrium. The instabilities have cover a representative selection of many macro-and micro instabilities in space plasma such as Rayleigh-Taylor instability, that the Rayleigh-Taylor instability is a macro instability type. We represented the general concept of instability and then we have specially pointed to the Rayleigh-Taylor instability. Also, after the introduction of one of the descxription model of the plasma as a fluid model, we have offer to the magnetohydrodynamic MHD equations as a dynamic model to introduce. The magnetohydrodynamic stratified plasma considered in absence of external magnetic field and then it have studied in presence of external magnetic field.