The fuel cap tightens against the fuel tank, creating an airtight seal. A rubber washer inside the cap makes this seal possible. If this rubber washer gets lost during a refueling stop, the tank and cap may start leaking fuel. The vibration from the engine can also gradually break down the cap's efficiency to maintain the airtight seal, which will also cause the mower to start leaking gas. If the cap looks cracked or broken in any way, replace it.
Two fuel hoses deliver fuel from the tank to the carburetor. These fuel hoses are made of plastic, which can degrade over time. As the fuel wets the hoses and dries off repeatedly, this will eventually degrade the plastic to the point that it becomes very brittle. If the fuel hoses get too brittle, they may crack or get punctured, causing fuel to leak from the system. Fuel hoses will need replacing at least every other season.
As the fuel hoses run from the tank to the carburetor, they connect at two different points. These connecting points also need an airtight seal for the gas to flow and not leak out of the system. The degradation of the fuel hoses can also cause these seals to break or come loose, leaking gas from the engine. When replacing the fuel hoses, use a press fluid to help lock the seal tight against the plastic hose. Always remove and install the hoses with your fingers and not a tool, which can damage the plastic.
When the fuel reaches the carburetor, it needs to get measured, mixed and then sent off to the combustion chamber. The inlet passages where the fuel enters can also get clogged or degrade, causing the fuel to back up in the system and leak out. Problems such as these may cause a leak anywhere in the fuel system. To fix these types of leaks, you will have to remove the carburetor and completely disassemble and clean it.