We present a method and organization of an arithmetic array processor for solving tridiagonal systems of linear equations. The method uses online arithmetic approach which allows parallel computation of the result digits of the solution vectors. The basic operators are digit-vector by digit multiplication and redundant addition which results in precision-independent cycle time. The method takes about m carry-free cycles to obtain m digits of the solutions. Details of a processor array organization implementing the method and a comparison with a conventional approach are discussed.