It is shown that the conventional mechanical-electrical analogy (velocity across→current through; force through→voltage across) has grave defects which have hindered its general adoption as a method of solving vibration problems. The new analogy however (velocity across→voltage across; force through→current through) can be safely applied in such a natural intuitive manner that it becomes unnecessary to distinguish between the mechanical system and the analogous electrical circuit. The problem solving techniques of electricity are taken over bodily into mechanics with the aid of the following devices: The mechanical systems are diagrammed with the aid of a set of conventionalized two-terminal symbols which picture the springs, mechanical resistors, and masses comprising the system. The letter symbols for velocity, force and mass are changed from the usual v, f and m to e, i, and c, respectively. A complex constant called the “mobility” (ease of motion) is defined as z = e/i = velocity/force and it is found that the mobility of the mechanical elements is of a familiar form (ze = jωl, zr = r, zc = −j/ωc) while series and parallel combinations of z's are made by the familiar rules. The solution of the mechanical problem is thus reduced to a determination of the mobilities at different points in the system and the application of the equation e = iz. The problem remains a problem in mechanics and there is no reference to electricity. Not only can forced vibration be computed in this manner, but the normal frequencies and normal modes of free vibration of resistanceless systems can be found. The concept of “acoustical mobility,” Z = E/I = volume velocity/sound pressure, permits the calculation of mechanical-acoustical systems.