Recent researches have indicated coupling between volcanic eruptions and earthquakes. Some of them calculated static stress transfer in subsurface induced by the occurrences of earthquakes. Most of their analyses ignored the spatial heterogeneity in subsurface, or only took into account the rigidity layering in the crust. On the other hand, a smaller scale heterogeneity of around hundreds of meters has been suggested by geophysical investigations. It is difficult to reflect that kind of heterogeneity in analysis models because accurate distributions of fluctuation are not well understood in many cases. Thus, the effect of the ignorance of the smaller scale heterogeneity on evaluating the earthquake triggering of volcanic eruptions is also not well understood. In the present study, we investigate the influence of the assumption of homogeneity on evaluating earthquake triggering of volcanic eruptions using finite element simulations. The crust is treated as a stochastic media with different heterogeneous parameters (correlation length and magnitude of velocity perturbation) in our simulations. We adopt exponential and von Karman functions as spatial auto-correlation functions (ACF). In all our simulation results, the ignorance of the smaller scale heterogeneity leads to underestimation of the failure pressure around a chamber wall, which relates to dyke initiation. The magnitude of the velocity perturbation has a larger effect on the tensile failure at the chamber wall than the difference of the ACF and the correlation length. The maximum effect on the failure pressure in all our simulations is about twice larger than that in the homogeneous case. This indicates that the estimation of the earthquake triggering due to static stress transfer should take account of the heterogeneity of around hundreds of meters.