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Practice has proved that drag reduction oscillators can decrease the axial friction and increase wellbore extension effectively in sliding drilling operations. However, the complicated mechanical behavior of drillstring with drag reduction oscillators has not been revealed sufficiently. In this paper, the mechanical model of drillstring with drag reduction oscillators is established by considering the friction nonlinearity. Further introducing the initial conditions, boundary conditions and continuity conditions, the finite differential equation of drillstring vibration is obtained and solved. The new model has been applied to a case study, in which the drag reduction effects of drillstring with and without oscillators are compared and the effects of relevant factors on drag reduction are analyzed. The results show that the hook loads increase obviously by reducing downhole average friction coefficient for drillstring with oscillators. Increasing vibration amplitude of the drag reduction oscillator can decrease axial friction, but the vibration frequency is nearly irrelevant to drag reduction. Increasing number of drag reduction oscillators can decrease axial friction, but may lead to large hydraulic power loss and high risk of drillstring fatigue. Therefore, there is an optimal number of drag reduction oscillators. The research results are of significant guiding significance for optimal design and safety control in sliding drilling operations.