Today, oil journal bearings are widely used as an efficient support for rotary systems in various industries. When these bearings are used by loading in high speed conditions, whirling disturbances in the rotor motion status leading to collisions and abrasion is probable. Designing specific geometric shapes or applying industrial lubricants with different new combinations can affect the journal bearings ability to maintain their dynamic stability in critical situations. From this view, the use of non-circular bearings and non-Newtonian fluids in the field of lubrication has recently been heavily taken into consideration. In the present study by choosing non-Newtonian lubricant simulated by power law fluid model, the effects of design parameters such as eccentricity ratio, aspect ratio and power law index on dynamic stability of noncircular two, three and four lobe bearings are investigated. For this purpose, assuming the limited cycle oscillations of the rotor around the equilibrium point after damping the effects of initial imposed disturbances and using finite element numerical method to solve the governing equations, stability range of the system in form of linear dynamic analysis characteristics is determined based on the whirl frequency ratio and critical mass parameter. The results indicate that by increasing the power law index and decreasing aspect ratio, the dynamic range of bearing support will be developed. Also, by increasing the number of noncircular bearings lobes with power law lubricant and providing the system's positioning conditions in high values of eccentricity ratio, more ability to damping dynamic disturbances can be achieved.