Based on coupledmode theory,the general model and characteristic euqation of metalcoated quadruple clad longperiod fiber grating gas sensors are established.The problem of overflow of the Bessel functions caused by the big imaginary part of the complex refractive index of metal is discussed detailedly.The solution is given by a programmed scaling of each step of the calculation of the Bessel functions.In addition,three procedures(the integral method,the power series,and the asympotic expansion) are discussed detailedly.