The stability of two-axial groove cylindrical journal bearing is improved by milling a step or pressure dam in the upper half surface and by cutting a deep groove or relief-track in the lower half surface. Dynamic analysis of elliptical bearings having similar construction of dam and relief-track, called elliptical pressure dam bearings, has revealed that these bearings are far more stable than ordinary cylindrical, cylindrical pressure dam, elliptical, three-lobe, etc., when supporting a rigid rotor. In this paper, the stability of finite elliptical pressure dam bearings supporting flexible rotors is discussed. The dimensionless rotor flexibilities selected are 0.5, 1.0, 2.0, and 4.0, which cover almost the entire range of practical interest. Effects of design parameters such as vertical preset, L/D ratio, Sommerfeld number, dam location and relief-track width ratio on the stability of these bearings, corresponding to various dimensionless rotor flexibilities are presented in the form of graphs. Also, the effect of turbulence over the entire bearing surface has been included. The bearings have been analyzed by finite-element method.