This paper applies method of theoritically analysis to prove the equivalent model of fused fibre compose wave guide. The weakly guiding and weakly coupling approximation must be utilized when the approximate parallel waveguide model takes the place of the original model of the fused tapered wave guide. According to this analysis and the technology of the weakly fused tapered by ourself we obtain that the high grade wide band couplers with a shape of dumbbell satisfy the weakly guiding and weakly coupling conditions.