Squeeze film dampers (SFDs) have long been used to attenuate the vibration of high-speed rotating machines such as gas turbine engines, turbo-chargers, etc. Due to their highly non-linear behaviour, it is often difficult to calculate the steady state vibration response of rotor-SFD systems. Over the years, methods such as the Runge-Kutta-Merson Method (RKMM) have been applied to solve the non-linear equations of motion for the system. However such a method requires huge amounts of computational time especially when a flexible shaft system is involved. In order to accelerate the calculations of the rotor-SFD system vibration response, the Modified Harmonic Balance Method and the Modified Iteration Method are introduced in this work. It is shown that their results agree very well with the RKMM predictions and the experimental measurements. The circumferential oil-feeding groove within the SFD radial clearance is designed to prevent oil starvation in the squeeze film. The pressure generated by the groove is traditionally neglected. To date, many experiments are designed to test SFDs with groove-depth to clearance ratios (cg/c) between 3 to 10 but no attempts have been made to assess the merits and weaknesses of various existing squeeze film force models under a wider range of parameters. In this work, the vibration responses of the SFDs tested with various groove depths (i.e. 340). These observations should be sufficient to provide useful guidelines for engineers to design a shallow or deep grooved SFD-rotor assembly. The SFD can be sealed to increase its damping. Empirical methods are commonly used to predict the vibration response but deeper understanding of the oil flow within the damper is not achieved. In this work, the flow balance principle is used to find the boundary conditions of the end-sealed SFD. With the assumption of a short bearing, averaging the one-land and two-land pressure distributions within the damper clearance, the current research shows that a good estimation of the end-sealed SFD vibration can be achieved. Such a model would be useful for the development of a comprehensive analytical end-sealed SFD model.