Abstract: This paper utilizes the nonlinear MHD code CLT to comprehensively investigate the influence of plasma aspect ratio, elongation, and triangularity on the linear growth rate of the sawtooth mode. The research reveals the following findings: (1) The aspect ratio increases leads to a decrease in the linear growth rate of the sawtooth mode. (2) The effect of elongation on the linear growth rate of the sawtooth mode is modulated by the aspect ratio. When the aspect ratio is small, an increase in elongation is not beneficial for the stability of the sawtooth mode, whereas when the aspect ratio is larger, elongation is beneficial for the stability of the sawtooth mode. (3) The linear growth rate of the sawtooth mode is modulated by positive triangularity as elongation increases. When the elongation is less than 1.2, an increase in positive triangularity enhances the growth rate, which is not beneficial for the stability of the sawtooth mode. However, when the elongation is greater than 1.2, an increase in positive triangularity significantly reduces the growth rate, which is beneficial for the stability of the sawtooth mode. (4) The variation of the linear growth rate of the sawtooth mode with triangularity is modulated by both the aspect ratio and elongation, and the relationship is complex. Overall, the simulation results indicate that the toroidal effect has a significant impact on the linear growth rate, and a combination of large elongations and positive triangularities are not beneficial for the stability of the sawtooth mode. The linear rata is modulated by the aspect ratio, elongation, and triangularity. This study provides valuable insights for the future design of advanced configurations for high confinement plasmas in a tokamak.