[Objective] For studing the function of surface tension which be used for distinguishing laminar flow or turbulent flow of thin sheet flow on slope surface.[Methods] The theoretical method of comparing acting force was adopted. Upon the basis of comparison between resistance of surface waves which embodies the surface tension(no rain) in the direction of motion

and viscous force

the quantitative relationships among wave length

wave height and depth of water were analyzed with reference to the data from test and numerical simulation results in the related literatures.[Results] (1) The critical Reynolds number used to distinguishing laminar flow or turbulent flow depended on Froude number(Fr)

roll wave length and wave height; (2) In roll wave occurrence condition (Fr ≥2)

the critical Reynolds number of thin sheet flow on slope surface was bigger than open channel flow.[Conclusion] The maximum of critical Reynolds number of the thin sheet flow on slope surface after roll wave occurred was 1.187 5 times of the corresponding value of open channel.