This paper presents the results of a dynamic investigation with the aim of determining both the optimal shape of an offshore gravity platform column and the required mass of the infill water. The natural frequency formulation of the structure with the added infill water mass, , was obtained by using Rayleigh’s method. Pontyagin’s maximum variational principle was used to define the shape of the column. An algorithm and a computer program were developed to obtain the numerical solution of the problem. Finally, a scaled model of the gravity platform was built and tested, in order to verify the results obtained from the analytical research and to determine the mass of the infill water.