The Squeeze film damper has proved a useful means of eliminating instabilities and reducing vibration in rotor-bearing systems. Analyses for this problem generally assume parallel land dampers. In this thesis, the pressure distribution, the fluid film forces, and the stiffness and damping coefficients of variable land geometry narrow, circular orbit type squeeze film dampers are obtained theoretically, assuming end feed and the Short Bearing Approximation. The coefficients for 7r film are obtained for quartic, exponential, cosine and step wise axial profile variation and compared to those for parallel axial land geometry. It is shown that variable land geometry dampers can reduce the variation of stiffness and damping coefficients, thereby reducing the degree of damper force non-linearity, and presumally reducing the likelihood of undesirable bistable operation. Alternatively, variable axial land geometry dampers can significantly alter the unbalance response, and in particular, the likelihood of undesirable jump of circular orbit type squeeze film dampers. This thesis investigates the effect of variable land geometry profiles mentioned above on the jump up propensity of such dampers. Theoretical investigation is restricted to n film vertical rigid rotors with end feed and the application of Short Bearing Approximation. It is found that regardless of unbalance and regardless of the depth, width or shape of the profile, parallel land dampers are least likely to experience jump up to undesirable operation modes. These conflicting conclusions might be accounted for by the reduction in damping, and in fact, the reduction in the pressure. Moroever, the damper model with end feed assumed in this thesis could alter pressure distributions and forces. Thus, these conclusions will need to be qualified for practical dampers with oil hole feed. Finally, the limitation of Short Bearing Approximation for large e region could alter actual unbalance response data.