In this paper a new method is suggested to calculate added mass coefficients of an underwater vehicle. In this method linear accelerated motion of the underwater vehicle is numerically simulated. Velocity and acceleration related forces, are extracted from the simulation results, from which the added mass coefficients are extracted. In order to validate the obtained results, initially, the added mass coefficients of an ellipsoid are calculated with the use of the present method and compared with the available corresponding analytical results. The obtained results from the suggested numerical method agreed well with those obtained from the analytical method, indicating that the present method can be used to obtain the added mass coefficients of more complicated geometries, including the underwater vehicle model constructed in Subsea Research and Development Centre. In addition, the numerically obtained results agreed well with the experimental results recently obtained, using the Planar Motion Mechanism tests conducted in Subsea Research and Development Centre.