Automated warehouses play a crucial role in developing modern logistics systems for moving goods. To increase productivity and effectiveness of warehouse use, stacker cranes need to have large dimensions, but this poses challenges in modelling and controlling. Previous studies often focused on approximating stacker cranes with a simple oscillatory motion, only describing the dynamics of the endpoint of the stacker cranes. This paper proposes the use of the Euler-Bernoulli beam model and applies Hamilton’s principle to construct a mathematical model with partial differential equations, boundary conditions, and constraints. The proposed model allows examining all points along the stacker cranes and is essential for developing control algorithms for stacker cranes. Simulations and comparisons to experimental results have been done to evaluate the accuracy and effectiveness of the proposed model.