This paper is concerned with the behavior of vibration absorbers attached to systems with uncertain properties. The uncertainties of the main system properties are modeled in a probabilistic sense by means of a Bayesian probabilistic interpretation. The structural systems considered in this study are simple systems modeled as one-degree-of-freedom oscillators subjected to a white noise base excitation. Due to the uncertainty of the main system properties, the classical deterministic minimization problem becomes a stochastic optimization problem. An optimization technique is implemented to solve this non-classical problem, and the absorber parameters as well as the optimum response of the system are obtained. These results are then used to assess the performance of the vibration absorber. It is found that parameter uncertainties may have a significant effect on its effectiveness. Finally, an alternative approach that improves the absorber efficiency, when uncertainties in the main system properties are considered, is presented in this paper.