This paper presents a method for calculating contact force between bodies on plane. At each integration time step, the proposed method finds expected contact point on their outlines and then calculates penetration, velocity of penetration and contact force. This paper adopts continuous analysis method and multi-point contact method to calculate contact force. To obtain the accurate expected contact point on their outlines, a new algorithm is developed. The accuracy of the proposed algorithm is demonstrated by comparing the numerical results of the proposed method and DADS.