In this study, over 40-year achievements of many foreign and Polish authors in the field of methods of optimizing the characteristics of automotive suspension systems have been used. A method of conducting the optimizing calculations, further developed by the author, has been presented and exemplified by calculations of viscous damping in the passive suspension system of a vehicle moving on an uneven road surface with a random profile. To determine the discomfort and safety hazard measures, a linear quarter-car model of the suspension system and the spectral transmittance analysis method were employed. The results have been shown in the form of a dimensionless objective function, which was taken as a criterion of optimization in respect of ride comfort and safety. The limitation of deflections of the suspension system has been taken into account, too. The graphic form of this function, whose argument is the dimensionless suspension damping coefficient, resembles the pictorial qualitative relationships, shown in many publications by other authors and facilitating the interpretation of final results of the optimization.