This thesis focuses on two-dimensional computational simulations of flows of two immiscible incompressible viscous fluids with surface tension, while fixed computation grid is used. Free interface between fluids is realized by the level-set method that is suitable to capture changes in the interface topology. The flow is described by the Navier-Stokes equations for incompressible fluids, numerical discretization is done by finite elements method with Q₂ - P₁ elements, while whole problem is solved as coupled. Several example simulations are presented, an overview of numerical examples and analysis results related to this topic is also provided.