Although heavy oils are an enormous resource and a common seismic monitoring target, their geophysical properties remain poorly understood. The shear modulus is of particular interest, because under the right conditions, these oils can transmit S-waves. However, there is a large uncertainty on how to measure the shear modulus of heavy oils. The use of the rheometer, common in chemical engineering applications, has been proposed as a good alternative to tension/compression techniques. Rheometers are an attractive alternative for measuring the shear modulus because of their widespread use and availability. In order to test the validity of the rheometer as a method to measure the shear modulus of heavy oils for geophysical applications, we tested two samples using techniques familiar to geophysics (tension/compression and ultrasonic) and compared the results with the rheometer measurements. We noticed a difference in the measured shear modulus between the two techniques. The samples showed a solid-like behavior when tested in the tension/compression equipment while behaving liquid-like in the rheometer. Both measurements were done in the linear regime (in which there is no change in modulus with amplitude), indicative of the potential presence of two linear viscoelastic regimes (LVRs) at different amplitudes. We developed a model that explains the presence of the two LVRs for heavy oils with a large content of resins and asphaltenes and at temperatures that allows the formation of large aggregates. We analyzed the presence of the two LVRs in terms of the weak interaction that appeared between aggregates when subjected to small-amplitude strains, resulting in a solid-like behavior; those weak interactions were not present when the sample was subjected to larger strains resulting in a liquid-like behavior.