A numerical method for simulating fluid–elastic solid interaction with surface tension is presented. A level set method is used to capture the interface between the solid bodies and the incompressible surrounding fluid, within an Eulerian approach. The mixed velocity–pressure variational formulation is established for the global coupled mechanical problem and discretized using a continuous linear approximation in both velocity and pressure. Three ways are investigated to reduce the spurious oscillations of the pressure that appear at the fluid–solid interface. First, two stabilized finite element methods are used: the MINI-element and the algebraic subgrid method. Second, the surface integral corresponding to the surface tension term is treated either by the continuum surface force technique or by a surface local reconstruction algorithm. Finally, besides the direct evaluation method proposed by Bruchon et al., an alternative method is proposed to avoid the explicit computation of the surface curvature, which may be a source of difficulty. These different issues are addressed through various numerical examples, such as the two incompressible fluid flow, the elastic inclusion embedded into a Newtonian fluid, or the study of a granular packing. Copyright © 2012 John Wiley & Sons, Ltd.