Trimming technique is a powerful and efficacious way of endowing an arbitrary complex topology to CAD files created by using NURBS. In the present work, it is shown that any complex multiply-connected NURBS domain can be described by using trimming curves only. lsogeometric analysis for linear elasticity problems of complex topology described in this way is presented. For fully communicative interaction between CAD and CAE, a specific searching algorithm and an integration scheme of trimmed elements are introduced to utilize the ICES files exported from CAD system for Isogeometric analysis. Schemes for imposing essential and traction boundary conditions on trimming curves are presented. It has been demonstrated that with the presented schemes trimmed cases in any complicated situations can be successfully treated. With the examples of complex topology that could be described by employing trimming curves only, effectiveness and robustness of present method are demonstrated. (C) 2010 Elsevier B.V. All rights reserved.