The work aims to solve the problem that the connection parts of rack and motor are frequently damaged when the load cell calibration device rack is subject to the impact load of weights and the motor vibration. By means of finite element analysis technology and in combination with 3D design software Pro/E, a model was built for the rack. Based on the theory of modal and harmonic response analysis, the finite element analysis software Ansys Workbench was used to analyze the harmonic response of the rack. The relationship between the external load frequency and the stress, deformation and strain of each part of the rack was obtained. It was determined that the dangerous frequency range of the load cell calibration device rack was 70.467 Hz and 77.92 Hz, i.e. the fourth and sixth order modes of the natural modal order. Through the harmonic response analysis, the maximum vibration amplitude that may be generated when the rack resonates is obtained, which provides certain theoretical reference for the load cell to avoid resonance in the actual work.