The generic expressions of those low order or efficient RRMSSM stiffness and mass matrices of the L-shaped structure have been reported. The L-shaped structure is a basic and important engineering structure. The inherent computational superiority of the RRMSSM is enhanced by these integrals because these reduce the number of computer operations. The implication of this work is that there now are available generic system matrices expressions that will allow the attainment of very accurate natural frequencies and mode shapes of the L-shaped structure through very-low-order eigen value problems. A generic expression of substructure-synthesis mass and stiffness matrices of the L-shaped structure allows easy and accurate computation of its natural frequencies and mode shapes through the solution of low-order eigen problems.