This paper presents research on methods of estimation of frequency response of linear and nonlinear quarter car suspension models used for research of vehicle vertical dynamics. Linear quarter car suspension model is widely used for estimation of comfort and safety performance of passive and semiactive suspensions. A lot of works on control strategies were published on the base of testing them using linear models. But the real suspension  - especially shock absorbers  - are non-linear in three aspects : static characteristics, hysteresis and the presence of friction. Testing linear suspension model is possible with the use of analytical  transfer function formulas but testing real suspension on a testing stand or even virtual but nonlinear suspension needs to use methods of transfer function estimation. Then it was necessary to design appropriate input signal allowing to get useful response signals. With the use of obtained frequency responses a method of linear estimation of nonlinear suspension for a given range of working condition was proposed.