The response of a single degree-of-freedom spring mass system connected to a vibration absorber with a friction damper and subjected to a sinusoidal excitation is considered in this paper. Two possible configurations of the friction damper, rigid and flexible, are explored in details. Optimization of the parameters of absorbers with both these damper configurations to minimize the peak value of the frequency response of the primary system is presented. Results from this minimax optimization approach are compared to the classical solutions for a vibration absorber with linear viscous damper.