The purpose of this paper is to propose a theoretical treatment of radiation trapping in a multiple lines coupled system in which coupling includes collisional energy transfer and cross absorption between the excited states. First, to describe the coupled system, the Holstein equation of radiation trapping is extended to an integral differential master equation group in which the vector and matrix form is adopted. Then by use of operator manipulations, the asymptotic solution in the form of a series expansion in terms of operators is presented. Finally, the asymptotic solution is reduced, leading to a result which can not only give the system a complete description, but also has far more advantages than the simple cut off solution. A numeral illustration of a two excited states system is also presented.