This paper is concerned with the problem of synthesis of (passive) mechanical one-port networks. One of the main contributions of this paper is the introduction of a device, which will be called the inerter, which is the true network dual of the spring. This contrasts with the mass element which, by definition, always has one terminal connected to ground. The inerter allows electrical circuits to be translated over to mechanical ones in a completely analogous way. The inerter need not have large mass. This allows any arbitrary positive-real impedance to be synthesized mechanically using physical components which may be assumed to have small mass compared to other structures to which they may be attached. The possible application of the inerter is considered to a vibration absorption problem, a suspension strut design, and as a simulated mass.