In this paper, a physics based compact model for drain current in fin-shaped tri-gate GaN metal-insulator-semiconductor high electron mobility transistors (MIS-HEMTs) is proposed. A positive threshold voltage shift is seen in these devices as a result of superior gate control of the channel by additional gates. The combined effect of top and side gates on channel charge density is studied with the help of TCAD and total current is modeled as the sum of two-dimensional electron gas (2DEG) and sidewall currents. The proposed fin-width dependent 2DEG current model is developed considering the effect of increased gate capacitance on threshold voltage of the device and side-gate depletion of 2DEG. The side-wall accumulation current is modeled to capture the sidewall channel conduction at higher gate voltages. The proposed model is completely analytical and does not require any iterations or fitting parameters in contrast to the available models discussed in the literature. Our model shows excellent agreement with state-of-the-art experimental data.