The adequate lubrication of engine parts is critical for the engine durability, and insufficient oil supply to various friction areas might result in catastrophic engine failure.However, when the environment temperatures are very low, the presence of oil between friction surfaces may be significantly delayed, especially during the engine start-up after a longer period of time when the vehicle was not driven. The capability of the oil pump to transport oil within the engine depends on the low-temperature rheological properties of oil, as well as the geometry of the passages.There are testing methods that estimate the ability of an oil to provide lubrication at low temperatures by measuring the yield stress and viscosity in controlled conditions (ASTM D4684, D5293, D5133), but they provide limited data generally used as a guideline for the selection of an appropriate oil.This paper presents a methodology to computationally estimate the time needed for the low-temperature lubricant to reach the lubrication circuit, using measured rheological properties of the engine oil. For this study, the oil properties were determined using a hybrid rheometer. At very low temperature, the lubricant behavior is strongly non-Newtonian, that in undisturbed state exhibits gel characteristics, and starts to flow only after a yield point was reached. This complex rheological behavior is generally difficult to model in computational codes. Since the time necessary for the oil from the pan to reach the oil pump is critical at start-up, an accurate multiphase modeling is needed. The approach shown in the present work permits to realistically model the oil behavior and get insight into lubricant flow inside a cold engine.