This paper presents a method for adaptive refinement within an integrated mechanically based CAE system. The system uses a mechanical B-spline finite element model for both geometric design and mechanical analysis. A technique for locally refining a solution by B-spline finite elements is presented. The key component in the proposed method is the linear coordinate transformation introduced into the refined element. The transformation is constructed in such a way that the transformed nodal configuration of the refined element is identical to the nodal configuration of the neighbor elements. Therefore, the assembly proceeds in the regular fashion, while the C/sup 0/ continuity is forced along the inter-element boundary exactly. The proposed adaptive refinement method has been implemented both for surface and solid design without substantial differences in technical complexity. Its feasibility as applied to sculptured surface and solid objects is demonstrated by several examples.