Research of interaction faetween’light and atomic system of two energy levels enables us to obtain some important knowledge, such as transition probability of the electron. Usually these equations can be solved using the method of perturbation approximation in quantum mechanics. Direct study on the analytic solution of these equations has been conducted by many reseaehers, but so far no one has obtained a satisfactory and simple form of analytic solution. This paper presents some simple analytic equations of transition probability of the electron under several different conditions, including damping and strong field. It provides some convenient mathematical formulas for the study of electronic transition process.