Simulation of coil embolization procedure enables doctors to practice or plan the procedure without any risk. This paper reports a method to construct the system matrix of the coil model to be used in such a simulation. The main issue is how to reduce the computation time required in constructing and solving the system matrix. The coil model is composed of serially-linked mass-spring elements. By exploiting the symmetry of the coil elements along the central axis, the transformation matrix can be simplified. This paper also proposed a method to realize the deformation of the coil model according to a rotational input.