The threshold of non-cohesive uniform sediment motion on a horizontal sedimentary bed, under a unidirectional steady uniform stream flow, has been analytically modeled using the following concepts: (1) The randomness of sediment movement is based on the randomness of the mean flow velocity and the particle position parameter, and the exposure angles follows the Gaussian distribution by analyzing the experimental data. (2) The correction coefficient of bed roughness has a definite physical meaning and it has a linearly proportional relationship with the coefficient of the bed area (the bed structure coefficient). The formula obtained using the present model has been compared with the formulas proposed by different investigators. The present results have an excellent agreement with the experimental data reported by other papers. The present model provides the accurate estimation of the threshold shields parameter and the threshold flow velocity for the initiation of bed particle motion.