International audienceA self-consistent theory of relatively thin anisotropic current sheets (TCS) in collisionless plasma is developed, taking into account the presence of a guiding field By (all notations are used in the GSM coordinate system). TCS configurations with a finite value of guiding field By are often observed in Earth's magnetotail and are typical for Earth's magnetopause. A characteristic signature of such configurations is the existence of a magnetic field component along the direction of TCS current. A general case is considered in this paper with global sheared magnetic field By = const. Analytical and numerical (particle-in-cell) models for such plasma equilibria are analyzed and compared with each other as well as with C...