Abstract The isogeometric analysis (IGA) of a physical domain employs an analysis model whose order of continuity is the same as the geometric model of the domain, i.e., the mesh of (finite and/or boundary) elements is an exact representation of the geometry. In IGA, the most used geometric representation form has been trimmed NURBS surface patches. However, a problem with trimmed NURBS is that surface patches may not join each other continuously, undesirably producing surfaces with small gaps. To avoid this situation, this project adopts watertight representations of surfaces, more specifically, T-splines and subdivision surfaces (SubD). These representation forms avoid such fillets and allow for local refinement. For T-splines, the nodes of the analysis model correspond to the vertices of the so-called T-mesh; for SubD, they are the vertices of the control point mesh resulting from a subdivision process, e.g. Catmull-Clark. In either case, the elements can be taken as Bézier surface patches associated with the faces of the control point mesh and derived from a process known as Bézier extraction. Given the relevance of T-splines in CAD/CAM and SubD in the animation industry, this project aims to employ such representation forms in the development of IGA models of elastic solids and shells, by using boundary elements (BEM) and Kirchhoff-Love finite elements (FEM), respectively. The purpose is to explore the GPU processing power to assess if the IGA can be used as a viable alternative simulation method in interactive Computer Graphics. The applications to be developed include analysis in solid mechanics problems and simulation in physics-based animations, e.g. cloth simulation. The development strategy involves the Bézier extraction of T-splines and SubD, the refinement of the control point meshes for boundary conditions, directly or resulting from collisions, and, finally, the implementation on GPU.