In investigating the behavior of subcomponents of a structural system, attention is often given to the matching of mobility or impedance at mounting or junction points. Thus, if the mobility at a point in a certain frequency range is of interest, the structure supporting that point might be a black box containing a structural model designed to duplicate the desired mobility. The paper discusses methods for arriving at models based on various forms of series solutions for mobility of linear systems. Models are presented for a particular example: a uniform, thin bar with free ends. Although it is well known that a model with a very large number of discrete elements would adequately represent a uniform bar, the purpose of the present study is to investigate the possibility of furnishing a model containing only a few elements. The mobility of combinations of the simple models is also presented. Improving accuracy of mobility results in better prediction of transient response. An example is included to show that a properly devised system with only a few degrees of freedom can be superior to systems having many degrees of freedom.