An intake system with an air cleaner case that is reduced in size with an enhancement in intake efficiency. A tubular tip end portion of a connecting tube provides a connection between the carburetor side and the air cleaner case with the tubular tip end portion being disposed in the air cleaner case. A tubular opening end portion is provided in an air cleaner element contained in the air cleaner case for connecting to the tubular tip end portion of the connecting tube. A large diameter portion is provided in a frame member serving as a core of the air cleaner element for supporting the tubular end portion and the tubular opening end portion in a condition wherein the tubular tip end portion and the tubular opening end portion are fitted to each other. The large diameter portion is larger in diameter than any other portion of the frame member.