Summary: This work develops an approach for numerical simulation of fluid flow through a domain with a complex geometry. We consider a finite element discretization of the Stokes-Brinkman equation for modelling the incompressible viscous flow inside a fluid-solid systems combined with Lagrange multiplier/fictitious domain and special spherical bubble functions. Well-posedness of the new method, a priori estimates, and convergence results are established. Results of numerical experiments are presented and compared to the other methods.