Helical flow in annular space occurs in drilling operation of oil and gas wells. The correct prediction of the flow of the drilling mud in the annular space between the wellbore wall the the drill pipe is essential to determine the variation in the mud pressure within the wellbore, the frictional pressure drop and the efficiency of the transport of the rock drill cuttings. A complete analysis of this situation is extremely complex; the inner cylinder is usualy rotating, the wellbore wall will depart significantly from cylindrical, during driling operation the drill pipe is eccentric, and the eccentricity varies with position along the well. Moreover, drilling muds present pseudoplastic behavior, the viscosity is a strong function of the deformation rate. A complete analysis of this situation would require the solution of the three-dimensional momentum equation and would be computationally expensive and complex. Models available in the literature to study this situation do consider the rotation of the inner cylinder and the non Newtonian behavior of the liquid, but assume the position of the inner and outer cilinders fixed, i.e. they neglect the variation of the eccentricity along the length of the well, and assume the flow to be well developed. This approximation leads to a two-dimensional model to determine the three components of the velocity field in a cross-section of the annulus. The resulting differential equations have to be solved by some numerical method. The model presented in this work takes into account the variation of the eccentricity along the well; a more appropriate description of the geometric configuration of directional wells. As a consequence, the velocity field varies along the well length and the resulting flow model is three-dimensional. Lubrication theory is used to simplify the governing equations into a non-linear, two-dimensional Poisson Equation that describes the pressure field. Lubrication model was validated by comparing the predictions to reported results on fully developed flow on eccentric annular space. The results show the effect of varying eccentricity, non Newtonian behavior and inner cylinder rotation on the flow field and on the friction factor.