The problem of measuring the linear viscoelastic (LVE) properties of polymers at low frequencies is a long-standing one, especially for fractional melt index polyolefins with broad molecular weight distributions and small time-temperature shift factors. A squeeze-flow apparatus utilizing Newton's interference rings was devised that could measure minute displacements less than 1/4 the wavelength of the light used. Maximum transient stresses achieved with the prototype ranged from 0.3 to 70.3 kPa. Its simplicity allows several samples to be run simultaneously under vacuum, minimizing degradation and cost, both critical considerations for long experiments. This paper covers the design of the prototype and results for polydimethylsiloxane at room temperature.