In order to injection mold parts at a constant flow front velocity in a mold cavity of an injection molding system, particularly where the mold cavity has a varying thickness along its length, mold modeling software is used to calculate the cross-sectional area as a function of the distance from the gate, percentage of fill, or length of the mold cavity. Based on that cross-sectional area, the mold modeling software determines an appropriate recommended ram force profile and/or melt pressure profile that would result in filling the mold cavity at a constant flow rate. An injection molding system is then operated according to the recommended ram force profile and/or melt pressure profile.