In a cooling system for a multi-cylinder engine, a main gallery is provided around outer peripheral portions of the plurality of cylinder bores upstream a block-side coolant jacket to commonly surround the cylinder bores, and an upstream coolant gallery is provided between the block-side coolant jacket and the main coolant gallery to separately surround each of outer peripheries of the cylinder bores. The upstream coolant gallery and the main coolant gallery is in communication with each other through a constriction communication passage provided around the outer periphery of each of the cylinder bores, and the upstream coolant gallery is further in communication with an upstream end of the block-side coolant jacket. The cooling system further includes a block-side and flange-surrounding coolant gallery provided in the cylinder block to surround an outer periphery of the outward flange of a cylinder liner, and a plurality of dispensing passages permitting the communication between said block-side coolant jacket and said flange-surrounding coolant gallery. Further, a jacket sidewall is disposed in the cylinder head inside at least one of opposite outside walls in an axial direction of a crank shaft to define a head-side coolant jacket.