The structure of the shear Alfve´n waves is investigated in a collisional plasma with shear. The fourth‐order equation obtained by combining Ampere’s law and the quasi‐neutrality condition is solved by the method of matched asymptotic expansions fork⊥ &rgr;s≫≪1 to obtain the dispersion relation. A hierarchy of damped, localized modes are found which can have either even or odd parity. The solutions basically have the structure of kinetic Alfve´n modes trapped between the two Alfve´n cutoffs on either side of the rational surface. The mode damping arises from Ohmic dissipation by electrons near the rational surface. The relation between these modes, microtearing modes, and the Alfve´n continuum is discussed.