Abstract. Two simulation methods, Equivalent-Circuit Model (ECM) simulation and Finite Element Method (FEM) simulation, are proposed for analyzing the time evolution of the shielding current density in a High-Temperature Superconducting (HTS) film that is part of a pellet container moving in an applied magnetic field. In the ECM simulation, Newton's equation of motion for the pellet container is solved together with the circuit equations equivalent to the governing equation of the shielding current density in the HTS film. On the other hand, it is solved together with the governing equation in the FEM simulation. Two numerical codes are developed on the basis of the ECM/FEM and the performance of the Superconducting Linear Acceleration (SLA) system is investigated by using the two codes. The results of computations show that, even for the case with a single electromagnet, the SLA system has a possibility to accelerate a pellet container up to over 140 m/s.