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The coining technology produces a wide variety of commemorative coins with exquisite patterns. However, it often encounters defects such as insufficient filling, flash lines, light bands, and so on. Process engineers usually perform multiple tryouts to avoid the above-mentioned problems in actual production. This is not only time-consuming and laborious but also ineffective. The virtual tryout of the finite element method (FEM) could assist engineers to avoid the defects in the coining process with a great improvement in product quality. In order to exactly describe complex patterns of commemorative coins, a large number of elements are employed in the classical FEM. Even then, the three dimensional elements, which come in early contact with the reliefs of the punch/die, undergo large deformation and become distorted. Errors of contact judgment between the tools and the workpiece in the FEM occur during the simulation process. Taking into account the advantage of Non-Uniform Rational B-Spline (NURBS) basis functions when accurately describing complex boundaries or surfaces, isogeometric analysis (IGA) is developed for studying the material filling of coin cavities. Six numerical examples involving elastic and plastic analyses with/without contact issues are considered by the presented IGA frameworks and show good performance of the present method in simulating the cavity filling compared with ABAQUS. In addition, numerical findings also indicate that the proposed method exhibits excellent contact detection and strong anti-mesh distortion in large deformation of the coining process. These encouraging observations motivate us to explore the NURBS description of complicated reliefs of coins and the corresponding IGA framework for the coining process. [ABSTRACT FROM AUTHOR]