The present work proposes a new computational algorithm for analyzing Morton Effect using a Successive Iterative Synchronous Response Algorithm (SISRA). Previous studies on the Morton Effect were based on Eigen or Nyquist analysis for stability studies and predicted only an onset speed of instability. The outcome of SISRA is the convergence of response to a steady state orbit in a finite number of iterations. A progressive increase in the response with increasing running speed indicates the former instability. SISRA predicts both the synchronous response for the speed range of concern plus the speed where the response becomes divergent. SISRA is implemented in a Timochenko-beam-based finite-element rotordynamics software suite. SISRA analyzes the Morton Effect as a synchronous response problem with excitations from: (1) mechanical imbalance, (2) induced thermal bent shaft moments, and (3) mechanical imbalance that is induced by thermal bow. A general elliptical orbit can be decomposed into the sum of forward and backward circular orbits. As input, SISRA requires that, at a specified speed, equilibrium position, and orbit: (1) the predicted maximum differential temperature, and (2) the angle between hot spot (position of maximum temperature) and position of minimum film thickness. Two examples from the published literature are considered. SISRA predicted higher vibration levels, even before the motion diverges due to Morton Effect. In some cases, the synchronous response of the system due to Morton Effect is orders of magnitude greater than the response due only to mechanical imbalance. The combined effects of: (1) mechanical imbalance with induced thermal bent shaft moments, and (2) mechanical imbalance with thermally induced mechanical imbalance are also studied. The impact of induced thermal bent shaft moments is found to be greater than the mechanical imbalance induced by thermal bow. A parametric investigation on the impact of the changes of (1) bearing length to diameter ratio, (2) reduced viscosity of the lubricant, (3) bearing radial clearance to radius ratio and (4) overhung mass magnitude is performed to consider their respective impacts on synchronous response. Based on the available input data and the cases considered, reducing viscosity and reducing the overhung mass are found to be the best remedies to alleviate problems arising from the Morton Effect.