In this letter, the dispersion of the MgF₂ wedge cavity is simulated using the finite element method and the dispersion effect of radius, wedge angle value, and wedge angle position on the full cavity in the communication band is studied. Further, the dispersion curve is used to simulate the frequency and time domains of solitons using the Lugiato-Lefever and thermal migration equations by employing the blue to red detuning process. The impacts of scanning speed, quality factor, and pump power on solitons are evaluated. Combined with previous experiments and assumptions, some important parameters of the MgF₂ wedge cavity for the soliton generation are discussed. The data results are useful for fabricating the MgF₂ wedge cavity with low anomalous dispersion and generating soliton combs in this cavity.