As for two dimensional added mass coefficients for straight framed hull forms in a free surface of an ideal fluid, theoretical calculations by F.M. Lewis, vertical, K. Wendel, J.H. Hwang, and etc. are available; vertical modes of rectangular and triangle sections by Lewis, vertical, horizontal and torsional models of rectangular and triangle section by Wendel, and systematical calculations for vertical modes of single chine forms by Hwang. In this paper, employing the conformal transformation by which a unit circle and its exterior region can conformally mapped to a polygon and its exterior region, the author calculated two dimensional added inertia coefficients systematically for straight framed sections with single chine in horizontal and torsional modes of vibrations. As the results, it was found that sloping side angle is an important factor measuring the magnitude of two dimensional added inertia coefficient for a set of given values of the sectional area coefficient and the beam-draft ratio. To grasp it cleary in physical sense, pressure distributions are investigated for some typical section contours. The numerical results are presented graphically in the form of two dimensional added sectional area coefficients with beam-draft ratios and sloping side angles as parameters, so that the data may conveniently utilized for estimation of the added inertia coefficients based on a three parameter technique.