Aquaporins are small ubiquitous membranes in biological channels that play significant role in the transportation of nano-sized materials, such as water and other biomolecules, into cell. The present work proposes a mathematical model to determine the potential energy of the interaction between a methane molecule and three different types of aquaporin channels, which are aquaporin-Z, aquaglyceroporin and aquaporin-1. We adopt a continuous model, where all atoms comprising the aquaporin channels are assumed to be uniformly distributed throughout their volumes. We also assume that a methane molecule comprises two parts: A single point representing the carbon atom at the centre and a spherical shell of four evenly distributed hydrogen atoms. Our results indicate the naturalistic acceptance of a methane molecule inside aquaglyceroporin and aquaporin-1 channels, but the repulsion occurs for the case of aquaporin-Z channel.