In this paper, we show how one can account for the incompressibility constraint within the multimodel Arlequin framework. The main issue is the treatment of a double constraining of the displacement fields in the gluing model zone. An elastic incompressible structure problem is considered. An incompressible Arlequin formulation of this problem is developed and supported by a stability and consistency result. Its discretization by means of mixed finite elements is detailed. The Inf–Sup condition is numerically discussed for different choices of the Arlequin method parameters. Several numerical tests are conducted and practical recommendations for appropriate choices of these parameters are clearly stated. Copyright © 2013 John Wiley & Sons, Ltd.