In practice, a torsional vibration absorber (TVA) is attached to the reciprocating engines to reduce torsional vibration stresses in resonances. A TVA comprises a rotating mass and a torsional spring, thereby generating a trough on the curve of amplitude of steady-state response and especially an absorbing point through the exact tuning the natural frequency of a TVA to the exciting frequency. In technical realization of a TVA at design stage, however, damping is always present somewhat or less in elastic material like rubber, so that the design of a linear TVA turns into a problem of optimization of the TVA-parameters in the operating frequencies. The use of practical objective functions and constraints which utilize the concepts and results of recent research, regarding one dimensional heat conduction in rubber, lead to a more careful consideration of the parameter values. A design procedure is presented from the results based on the numerical analysis.