The working principle of a ball-screw inerter was analyzed regarding its nonlinear mechanics characteristics. A nonlinear mechanics model with friction, backlash and elastic force of screw was built based on the analysis of the major components of the ball-screw inerter. The mechanical responses of the ball-screw inerter were obtained by testing a ball-screw inerter with different inertances and excitation inputs using a CNC hydraulic servo exciting test-platform. Based on the testing results, the influence of friction and backlash on the mechanical performance of the ball-screw inerter was investigated, and a mechanics model with easily identifiable parameters was obtained with the simplification of friction and backlash. According to the experimental data, the parameters of the ball-screw inerter mechanics model were identified through the recursive least squares algorithm. Comparison of the simulation and experimental results of the ball-screw inerter output force showed that the root mean square value error of the output force in one period was less than 7%, which proves the efficiency of the proposed method.