Linear harmonic vibration during machining of a conical journal may produce micron order undulations on outer surface of journal. Further, a lubricant comprising of long chain polymer additives may attain polar effect due to couple stresses. At high pressure conditions, pressure viscosity interaction in oil may affect the actual viscosity of the lubricant. The flow behaviour of piezoviscous-polar lubricant in a conical bearing is modelled in cylindrical coordinates. FE analysis is utilized to solve the modified Reynolds equation. The results indicate that journal undulations offer relatively higher oil film pressure due to local convergence in oil film, consequently exhibit higher stiffness coefficients. Moreover, piezoviscous-polar lubricant may raise the values of S ¯ z z upto 18% and C ¯ z z upto 32% than Newtonian lubricant.