Greasing is the preferred lubrication method in many mechanical devices. To simplify the design, some systems use multiple branches so that the grease must go through channels or different restrictions to reach target spots. Conceptually, flow restriction can be included in the design to achieve optimal grease distribution, but the detailed design can be complicated. For example, appropriate dimensions of various machine elements and their manufacturing tolerances must be considered along with the property of the grease, its feeding device, and its seal design. Currently, grease-feeding design relies heavily on experimental tests. A system-level modeling and analysis is desirable to understand the sensitivity of design parameters to the overall lubrication performance. In the study of grease lubrication of a universal joint, we have developed a semi-empirical model to address this challenge. The model is found useful to provide design guidance. The methodology can be extended and applied to more complicated cases. Laboratory tests on grease flow rates were conducted for a number of design alternates. Based on these data, the functional relationship of an equivalent discharge coefficient and the system parameters can be determined. Charts generated by the analytical model provide designers with a convenient tool for making design decisions.