By superposing and gluing models, the Arlequin method offers an extended modelling framework for the design of engineering structures. This paper aims at developing the numerical aspects of the approach and at showing how it can be used with great flexibility and in a consistent manner to change locally a global mechanical model. The capabilities of the Arlequin method and the effectiveness of the implemented numerical tools are exemplified by 1-D, 2-D and 3-D numerical applications.