The origin of the long secondary periods (LSPs) in red variables remains a mystery until now, although many models exist. The light curves of some LSP stars mimic an eclipsing binary with a pulsating red giant component. To test this hypothesis, the observational data of two LSP variable red giants, 77.7795.29 and 77.8031.42, discovered by the MACHO project from the Large Magellanic Cloud, are collected and analyzed. The probable eclipsing features of the light curves are simulated by the Wilson-Devinney method. The simulation yields a contact and a semidetached geometry for the two systems, respectively. In addition, the pulsation constant of the main pulsating component in each binary system is derived. By combining the results of the binary model and the pulsation component, we investigate the feasibility of the pulsating binary model. It is found that the radial velocity curve expected from the binary model has a much larger amplitude than the observed one and a period double the observed one. Furthermore, the masses of the components based on the density derived from the binary orbit solution are too low to be compatible with both the evolutionary stage and the high luminosity. Although the pulsation mode identified by the pulsation constant which is dependent on the density from the binary model is consistent with the first or second overtone radial pulsation, we conclude that the pulsating binary model is a defective model for the LSP.
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