A fractional‐derivative Maxwell model is proposed for viscous dampers, which are used for vibration isolation of piping systems, forging hammers, and other industrial equipment, as well as for vibration and seismic isolation of building structures. The development and calibration of the model is based on experimentally observed dynamic characteristics. The proposed model is validated by dynamic testing and very good agreement between predicted and experimental results is obtained. Numerical algorithms for the solution of the constitutive relation in either the frequency or the time domain are presented. Some analytical results for a single‐degree‐of‐freedom viscodamper system are presented. These results are useful to the design of vibration‐isolation systems. Furthermore, an equivalent viscous oscillator is defined whose response is essentially the same as that of the viscodamper isolator. Finally, the model is employed in the analysis of a base‐isolated model structure that has been tested on a shake table.