Every object in nature has an infinite number of vibration frequency and amplitude as called “Natural Vibration Frequency”. Developing computer capacities allow calculating of natural frequencies and shapes of complex structures more accurate and understandable. In this study, a dual-trolley (2×400 tons) heavy-duty overhead gantry crane that can carry loads up to 800 tons was analysed by mathematical and finite element methods. The mathematical method is based on Euler-Bernoulli transverse vibration approach. On the other hand, finite element method is one of the most common numerical methods that can solve many engineering problems in a range from solid mechanics to acoustic. The generated solid model was analysed by the finite element method with the help of ANSYS Workbench 14.5 which is a commonly used analysis program. The obtained values of natural frequencies at mathematical calculations and finite element analysis were compared and presented.