The hydrodynamic bearings are important components of most of the rotary parts in different applications. The current study examines the performance of the traditional type, which is the most common because they are easy to the manufactured, relatively low cost, but they have low stability compared with other type because they have large values for the cross coupling stiffness coefficients, which are responsible for the whirl phenomenon. The mathematical model was constructed and the equations of the thickness change oil film were presented. In addition to the mathematical formula of Reynolds equation, the numerical solution was adopted to solve it using a (five-nodes) scheme method and it is solved using the (MATLAB) software. The oil film and the foundation were considered as springs that were connected to each other in series and the equivalent stiffness coefficient are calculated. The results showed that taking the foundation effect into account reduces the overall values of the stiffness coefficient. The results showed that the use of different materials in the covering leads to a decrease in the equivalent stiffness coefficient value depending on the layer thickness of the covering. The method of partial covering caused an important of some of stiffness coefficient and decrease..