The telescopic boom was treated as a variable section and variable length beam with concentrated parameters, pined at the end and flexibly supported in the middle, in order to investigate the luffing transverse plane dynamic behaviors of aerial work platforms during telescopic motion. Firstly based on Newton’s second law of motion, the differential equations of each arm were established. And then transient mode functions at a series of time points were obtained by using mode superposition method and boundary condition. After that the time-varying parameters of the mode function were fitted to approximately represent the mode of the beam. The state space equations of generalized coordinates could be built in terms of Galerkin truncation method. At last, the luffing plane transverse vibration response dynamic response of boom’s tip was simulated by using Matlab/Simulink during telescopic movement. Results show that as far as the amplitude of lateral vibration is concerned, the simplification of the connection situation will bring the calculation result error of 15.63%, and the simplification of support situation will increase the stiffness of the boom and reduce the response of vibration of the boom, which is not desirable.