This paper proposes a 3-D dynamic simulation of a previously developed basilisk lizard inspired quadruped robot, which is capable of locomotion on the surface of water. Using this 3-D simulation along with several 1-D and 2-D models, stability in terms of robot elevation from the water surface and robot rolling are examined. Analysis of the lifting force shows the robot is capable of running on water using viscous drag forces. Using this analysis, a criterion for convergence to a steady state distance from the water is presented. It is determined that 7-12 Hz is an appropriate running frequency range for the robot to lift its weight. Compliant footpads are found to be beneficial in reducing the force associated with pulling out of the water. Further, from the roll motion analysis, previous designs result in instability along the roll axis. By comparing leg running frequency to the body's roll frequency, the minimum required roll moment of inertia for stable roll motion can be determined.