Many high-precision measurement and control devices must be mounted on vibration-free platforms. Accuracy of those devices' output are adversely affected by the base excitation motion, so motion of these platforms must be isolated from the excitation source. In this paper, a flexible platform, which is mounted on a car, is considered as a base on which many such measurement and control devices can be attached. To this end, mixed finite element and lumped parameter model of the platform and vehicle are used to derive the model of such a system; this results in a discrete-model with finite degree of freedom. This lumped parameter model of the system is then controlled by a linear quadratic regulator, which minimizes the amplitude of vibration at finite number of points on the platform. The mathematical model of this system was simulated on a computer and it has been shown that it is possible to minimize the vibration of this flexible platform.