When dealing with the oscillations of fixed-base structures or machines induced by external forces, suppressing the vibrational impact on the adjacent structures and the environment helps to maintain the structural durability and ensure the users’ comfort level. This study proposed an inerter-based optimal solution to suppress the vibrational forces and energy transmitted to the supporting ground by utilizing the great potential of the inerter. For the external force, which contains various frequency bands, the stochastic response and an energy balance analysis are conducted to evaluate the force transmissibility, structural displacement, and vibration power flow. Given the benefits of the inerter, a transmitted-force-based optimal design framework is proposed for inerter systems, of which the effectiveness is validated by numerical examples. The obtained results show that inerter systems are capable of providing significant reductions in the structural displacement and the force transmitted to the supporting ground. Particularly, the closed-form power equation indicated that a grounded inerter can suppress the force transmission and vibrational energy, thus leading to a less negative impact on the ground and environment. Revealing the working mechanism and optimal design strategy of the inerter can help solve the force-transmission control problem experienced by some practical structures.