This paper deals with one kind of dampers which is inerter damper, Inerter is a new mechanical element proposed by Professor Malcolm C. Smith from Cambridge University, which is defined as a mechanical two-terminal, one-port device with the property that the equal and opposite force applied at the terminals is proportional to the relative acceleration between the terminals the principle work of inerter damper is how to convert the linear motion into rotational motion to mitigation the external excitation. Theoretical analysis was presented first part is the analytical study which made modeling for the damping structure proposed and get the equation of motion for the inerter behavior, secondly numerical analysis where the program (ANSYS WORK-Bench 18.2) was adopted, and study the parameters which effected on the damping behavior of inerter structure proposed that is (stiffness, coefficient of friction and mass of flywheel). Where it was found that when the stiffness of the springs increased gradually from (0.2, 0.3, 0.4, 0.6 and 0.8) Kn/mm the amplitude reduced from (25.791, 17.194, 12.896, 8.5974 to 6.4482) mm respectively for each stiffness reading, also the mass of inerter when increased gradually (200,400,600,800 and 1000) g with a constant coefficient of friction and constant stiffness 0.4, 0.6 Kn/mm respectively, the amplitude decrease from 6.3525 to 4.036290. Finally, to study the effect inerter mass on the structures, the mass of inerter increased from (200,400,600,800 to 1000) g gradually to the constant cantilever mass structure equal to 130g. The ratio of the inerter mass to the threshold mass is approximately 1.5 to 7.5 As results obtained from the previous study, the amplitude obtained for each mass (1.0778, 1.069, 1.0509, 0.9514 to 0.872) respectively