In this paper, the author describes a practical method, that is called the hypercircle method, of estimating the transverse added mass of two-dimensional bodies moving in restricted waters. This method is one which rather assesses the upper and lower bounds of the added mass than to calculate the added mass itself directly. However, in order that this method may be available in engineering applications, it is necessary for the upper and lower bounds to be near to each other. Hence, some illustrative calculations of the upper and lower bounds were conducted for the two-dimensional bodies with the sectional form of simple geometry, to say for some rectangular cylinders and a triangular one. Consequently, this method proved to be very useful in case of the rectangular cylinder, while this was not true of the case of the triangular cylinder because of the great difference between the assessed upper and lower bounds. On the other hand, however, it was found by comparing the bounds calculated by this method between the added mass obtained by other method, that is the finite element method, that the lower bound itself could give a good approximate value of the added mass.