In this paper, Lyapunov theory for uniform practical asymptotic stability (UPAS) is presented and utilized to solve the problem of position control of a planar underwater snake robot (USR). First, a precise definition of UPAS is presented, which imposes that, locally, all solutions converge to the origin up to a steady-state error that can be arbitrarily reduced by a convenient parameter tuning. Additionally, a sufficient condition for UPAS of a time-varying nonlinear system and a theorem for UPAS of cascaded systems are presented. These are then utilized to design controllers that stabilize the position of an USR when approaching from such a direction that the USR moves against the current. Results from numerical simulations are then investigated to validate the theoretical results.