Abstract: Many gastropods, such as slugs and snails, crawl via an unusual mechanism known as adhesive locomotion. We investigate this method of propulsion using two mathematical models, one for direct waves and one for retrograde waves. We then test the effectiveness of both proposed mechanisms by constructing two mechanical crawlers. Each crawler uses a different mechanical strategy to move on a thin layer of viscous fluid. The first uses a flexible flapping sheet to generate lubrication pressures in a Newtonian fluid which in turn propel the mechanical snail. The second generates a wave of compression on a layer of Laponite, a non-Newtonian, finite-yield stress fluid with characteristics similar to those of snail mucus. This second design can climb smooth vertical walls and perform an inverted traverse.