Liquid-filled cylindrical tanks are extensively used in industrial facilities, including petroleum, chemical, water supply, and nuclear power systems. These structures are frequently subjected to dynamic excitations caused by earthquakes, impact loads, and operational vibrations, which significantly influence their structural integrity and serviceability. The interaction between the contained liquid and the flexible tank wall alters the dynamic characteristics of the system by introducing additional inertia and fluid–structure coupling effects. Therefore, accurate prediction of the natural frequencies of partially filled tanks is essential for safe and reliable structural design. This study presents a dynamic free vibration analysis of a partially filled thin-walled cylindrical shell with one end fixed and the other end free. The fluid is assumed to be incompressible, inviscid, and irrotational, while the shell behavior is modeled according to thin shell theory. The governing equations are derived using the Rayleigh–Ritz energy method combined with Lagrange's equations. The fluid contribution is incorporated through the added-mass formulation obtained from the solution of the Laplace equation for the fluid domain. Numerical simulations are performed for both steel and concrete cylindrical tanks considering different liquid height ratios and shell geometric parameters. The results demonstrate that the natural frequencies increase as the liquid filling height decreases. Furthermore, increasing the shell height-to-radius ratio also leads to higher natural frequencies for both the first and second vibration modes. The proposed formulation provides an efficient analytical framework for evaluating the dynamic characteristics of liquid-filled cylindrical tanks and can serve as a practical tool for preliminary structural design and vibration assessment.