As a new type of semiconductor fiber, silicon-core fibers have a higher non-linear effect compared with silica fibers. Forward-stimulated Brillouin scattering as a typical optical non-linear effect holds strong promise for applications in, for example, fiber-optic sensing. The study of the FSBS effect in silicon-core fibers facilitates further theoretical exploitation of the potential of FSBS in fiber-optic sensing. In this paper, the FSBS in the silicon-core fiber is studied using the finite element method. The model is based on a silicon-core fiber, whose silicon-core diameter is 4 μm and silica cladding diameter is 33.4 μm, and the optical field modes are classified by the vector method to obtain the acoustic field modes excited by FSBS—radial mode (R0m) and torsional radial mode (TR2m). The FSBS gain of the fiber shows that R0m has the best coupling with TM and TE optical modes, and TR2m has the best coupling with HE optical modes. It is concluded that the sound field frequency shift of R0m is more sensitive to the change in the effective refractive index of the optical field than that of TR2m. The factors affecting the gain are refined into photoelastic effects and moving boundary perturbations, and their contributions to the total gain are summarized. Finally, it was confirmed that a strong FSBS gain similar to 365.57 (1/mw) can be obtained with silicon-core fibers without the need to reduce the size to the usual dimensions of silicon waveguides, paving the way for further research studies in areas such as frequency-tunable laser emission, mode-locked pulsed lasers, low-noise oscillators, and optical gyroscopes.