A model based on the response of a micro-rheometer which permits the measurement of the linear viscoelastic properties of small volumes of a fluid is described. The configuration involves a liquid being contained within a capillary bridge between two flat smooth parallel platens that are actuated sinusoidally using a compliant MEMS device. Approximate closed-form equations are derived to analyse the data taking account of both the capillary forces and those arising from viscoelastic flow. The approximate theory is compared to a full numerical simulation of the response of the MEMS rheometer and the validity is discussed.