The problem of effcient modeling and computation of the nonlinear interaction of fluid with a solid undergoing nonlinear deformation has remained a challenging problem in computational science and engineering. Direct numerical simulation of the non-linear equations, governing even the most simplified fluid-structure interaction model depends on the convergence of iterative solvers which in turn relies heavily on the properties of the coupled system. The purpose of this paper is to introduce a distributed multilevel algorithm with finite elements that offers the flexibility and efficiency to study coupled problems involving fluid-structure interaction. Our numerical results suggest that the proposed computational methodology for solving coupled problems involving fluid-structure interaction is reliable and robust.