Permeability tensor is a key parameter for Resin Transfer Molding (RTM) of fiber reinforced plastics as well as for its simulation. For sheared textile composites such as woven and knitted fabric composites after preforming or draping, the permeability tensor includes non-diagonal components which can not be measured easily. This paper describes a numerical evaluation of permeability from both macro- and microscopic standspoints for sheared plain woven fabrics. The asymptotic homogenization theory for solid-fluid mixture is employed to characterize the micro-macro coupling effects. The nature of the macroscopic permeability tensor is discussed first. The microscopic flow field is next evaluated in detail by various ways. The differences of the microscopic flow field was recognized between the undeformed and sheared fabrics. The effects of the macroscopic pressure gradient is also discussed.