Abstract: According to a continuous equation of the belt conveyor,a partial differential method was applied to dynamically analyze complicated problems existed. The elastic continued dynamics equation was established. Based on the D' Alemberts principle applied to analyze the elastic fluctuation features,the paper revealed the transmi ssion and reflection propagation features of the elastic wave at the second branch boundary of the belt conveyor. The features with a sum of the reflection coefficient and t he transmission coefficient being one were obtained. Thus a longitudinal fluctuation dynamics model of the belt conveyor was established. The limit dynamic tension occurr ed in the starting and braking process of the belt conveyor was solved under the different performances of a heavy hammer tension at the conveyor head. The non- slippin g condition occurred in the stating and braking process of the belt conveyor was derived.