Abstract: A novel multi-domain boundary element method (MDBEM) analysis technique is presented to solve large-scale engineering problems. Firstly, the basic integral equations of each domain formulated in terms of internal, boundary and interface nodal variables are reduced to the algebraic equations in terms of interface nodal variables only by the three-step variable condensing technique. Then, a sparse system of equations formulated in terms of interface nodal quantities is assembled using the equilibrium equation and consistence condition at interface nodes. To solve the system of equations efficiently, this paper, for the first time, introduces a robust linear equation solution method, called the row elimination-back-substitution method (REBSM), to solve the non-symmetric sparse system of equations. REBSM performs both the elimination and back-substitution procedures when each row of the system is formed. When the last row is finished for assembling, the solutions of the system are obtained at the same time, without the need of the last back-substitution procedure. Since some repeated terms are incorporated, REBSM needs less storage than the Gaussian elimination method, has an improvement in computational speed by orders of magnitude, and provide BEM a robust equation solver for solving large engineering problems.