The issue of added mass has often been misinterpreted and it is an important issue in the context of modeling bubbly flows where the added mass of the fluid dominates the inertia associated with bubble acceleration. This paper constitutes a thorough effort at identifying the forms the added mass coefficient, C, can take under various conditions. The paper can be divided into two sections : the first generalizes the cell model used by Zuber (1964, Chem. Engng Sci. 19, 897-903) and obtains various forms of C relating to a parameter lambda, the "external impedance". The versions of C suggested by Zuber (1964) and Wallis (1989, Multiphase Sci. Technol. 5, 239-361) become two limiting cases; the second develops an argument in terms of the equation of motions due to Wallis (1989) to arrive at the added mass, and its dependence on the boundary conditions. For the few sample cases studied, the characteristics of boundaries are found to be described by lambda. Therefore, a general link between the added mass in various two-phase flow situations and one sphere moving inside a concentric shell is established.