The problem of viscous fluid flow interacting with elastic body which goes under deformation with the fluid action is experienced in many real-life applications of great importance. Typical examples in biomechanics are cardiovascular problems, brain aneurysm, aorta flow problem, stenosed plaque problem and many more. Moreover, great challenges lie in this discipline due to vigorous non-linearities and the complex nature of the human structure, i.e., arterial walls are composed of three layers: media, intima, and adventitia, each with different elastic properties, and blood itself is a two-phase flow. A stable and efficient FSI solver that simulates the interaction between an incompressible, viscous fluid and a single/multi-layered structure would be an indispensable tool for the computational investigation of solutions. We present a method for solving a problem followed by some applications of fluid structure interaction of an incompressible elastic object in a laminar incompressible viscous flow. The method is based on a fully implicit, monolithic formulation of the problem in the arbitrary Lagrangian Eulerian formulation. A stable P2P1 finite element is used to discretize the problem and the resulting nonlinear algebraic system is linearized by implementing Newton's procedure. Finally, the linear saddle point type problem is solved by using geometric multigrid method.