Crawling through various terrains has been a long research interest. In recent years, quite a number of soft crawling robots have been developed. However, locomotion in an elastic, humid and slippery environment remains a challenge. In nature, gastropods, such as snail, live in humid environment and could crawl through all kinds of surface conditions by using wet adhesion. In the wet adhesive locomotion, the mucus is crucial in adhering the gastropod while allowing forward motion. Previously, we presented one snail-like soft robot that mimics the gastropods. In this work, we propose a second version and presented a theoretical model of the mucus simulant. In addition, the dynamic model of the soft robot’s wet adhesive locomotion is developed for the first time. In the modeling, a shallow BP neural network was employed to solve the nonlinearity of the soft actuator. The developed models helped speeding up the robot’s velocity. Results show that the speed of the current version is 5 times than that of the previous one. Also shown by the results that the mucus helps to speed up the robot by at least 2.7 times.