This thesis deals with the realisation of the inerter using a negative acceleration feedback loop. The first part of the thesis presents a short review of modelling of vibration systems, passive vibration control techniques and the working principle of the inerter with examples of the existing realisations of the device. A mathematical model with two mechanical degrees of freedom (DOF) is derived and expanded to include the dynamics of both sensors and actuators. The impact of the sensor-actuator dynamics on the stability of the feedback loop is studied. It is shown that the active control system is unconditionally stable if the dynamic behaviour of the sensors and the actuators is neglected and that the system becomes conditionally stable if these dynamics are taken into consideration. A numerical model using the finite element method with 100 DOF is also developed both neglecting and considering the sensor-actuator dynamics. Modal analysis is conducted using this model and its results are used to calculate transfer functions needed for the comparison. Mathematical model with 2 DOF is compared to the finite element method model with 100 DOF. Both mathematical models are also validated experimentally. The experimental setup is fabricated using a fused deposition modelling (FDM) technology and is equipped with accelerometers and electrodynamic (voice coil) actuators. Closed loop transfer functions are measured in order to determine the maximum achievable inertance. Open loop transfer functions were also measured for the evaluation of the stability of the feedback loop. The measurements reveal that the stability of the feedback loop is very sensitive to the dynamic behaviour of the sensor/actuator transducers.