The use of voltage induced strain to switch magnetic tunnel junctions (MTJs) is a promising solution for reducing the switching energy in MRAM technologies. The MTJ is integrated with a piezoelectric layer to generate the strain. A very thin layer is needed to switch with small voltages and small energy dissipation. It is challenging to synthesize ultrathin piezoelectric layers that retain a high degree of piezoelectricity. An alternate approach is to use time-varying strain generated by a surface acoustic wave (SAW). This approach does not require a thin piezoelectric layer since the SAW is confined to the surface of the layer. In this study, we fabricated in-plane MTJs on piezoelectric LiNbO3 substrates and used IDTs to generate the SAW signal within the substrate. Our results showed that the SAW signal had a significant influence on the resistance and the tunneling magnetoresistance (TMR) ratio of the MTJs. The influence was much less significant in nanometer size MTJs than in micrometer sized ones. Most surprisingly, the SAW signal caused the tunneling magnetoresistance ratio (TMR) to drop below zero for the micrometer size MTJ, meaning that the antiparallel resistance RAP is temporarily less than the parallel resistance RP under SAW excitation. Our results provide insight into the dynamic behavior of MTJs under periodic strain and the dependence of this behavior on the device dimensions as they are scaled down to nanometer sizes.