In this paper, analytical and numerical analyses of radial and tangential velocities and pressure of lubricant film have been considered in an eccentric journal bearing. A 2D flow of shear-thinning viscous fluid is followed by Carreau-Yasuda mathematical model between two eccentric cylinders. The model is mathematically conserved from eccentric coordinate to concentric coordinate due largely to easy solution. Therefore, the PDE equations were converted to the ODE equations with a set of nonlinear algebraic first order equations with their boundary conditions. These kinds of equations are called boundary value problems (BVP) that can be solved with shooting method. The results are compared with 2D numerical simulation in the Fluent software. Lubricant tangential velocity and pressure distributions are examined in the dynamic journal bearing. The comparison of the results revealed that numerical analysis as same as analytical approach is a reliable method for determining lubricant motion in the gap.