Using extended Hamiltonian variational principle, the governing equations for sloshing response of floating roofed storage tanks are derived. The response of the floating roofed storage tanks is evaluated for different types of ground motions, including near-source and long-period far-field records. Besides comparing the response of the roofed and unroofed tanks, the effect of different ground motions on the wave elevation, lateral forces, and overturning moments induced on the tank is investigated. It is concluded that the dimensionless sloshing heights for the roofed tanks are solely a function of their first natural period. Also it is shown that while long-period far-field ground motions control the free board height, near-source records give higher values for lateral forces and overturning moments induced on the tank. This means that same design spectrum could not be used to evaluate the free board and lateral forces in the seismic design of storage tanks. Finally, two cases are studied to reveal the stress patterns caused by different earthquakes.