Structures are always vulnerable to damage during operation. Therefore numerous iections on structures are carried out to identify the damage done to them. Steel storage tanks are one of the most widely used structures for long life which, due to their sensitivity, studying their dynamic characteristics is important. These tanks are almost exposed to destructive factors such as collisions, corrosion, and fatigue. Creating and propagating the cracks in the steel tanks reduces their life and causes great damage to the structure. The repair of minor damage is low cost and has fewer problems than global damage and can be implemented without interruption in the operation. Hence, identification of defects in tanks, including cracks, is very important before the propagation. One of the common damage identification methods is modal analysis. In this way, the geometric position and depth of cracks are identified by the vibration analysis. In the present study, the dynamic characteristics of flexible fluid tanks were estimated and the effect of crack was assessed. The choice of the appropriate mathematical model of the structure and crack is very important for crack identifying. For this purpose, the problem is solved for a simple supporting plate, then these equations are expanded for the rectangular fluid tanks. To approximate the displacement of plates by assuming the flexural theory of thin plates, polynomial and trigonometric triangular functions are used. Using the energy method, the energy of the vibrated plate in a perfect and imperfection state due to cracks presence is calculated with respect to the size of the crack and its depth. Using the Rayleigh-Ritz method and the matrix of mass and stiffness of the plate for both cases were extracted. The characteristic equation of the tank is formed and the natural frequency changes due to the crack were estimated. The governing equations governing the fluid vibrations were obtained by solving the Laplace equation and satisfying the boundary conditions of the fluid. The results show that natural frequencies decrease with increasing crack size. On the other hand, changing the position of the crack changes the natural frequencies. To evaluate the accuracy of the used method, numerical results were compared with the other results of the references. One of the innovations in this study is the ability to model several cracks in the plates and the applicability of the proposed theories in the damage identification for flexible fluid tanks. The results show that proposed computational equations provided to estimate the effect of crack on the mode shapes. For the case studies of possible comparison of results with the other studies, displayed that the errors in calculations in all cases were less than 3%. Keywords: Cracked Thin Steel plates, Rayleigh-Ritz Method, Cracked Rectangular Tanks, Liquid-Tank Interaction, Hydrostatic Vibration, Modal Analysis