In this article, the analytical modeling of a Vortex Robotic Platform (VRP) is investigated. Following the design of the Vortex Actuation (VA) unit and VRP presented in authors' previous work, the target goal is focused on providing a modeling methodology to include system dependencies on surfaces of different curvatures and robot orientations. The critical force model for guaranteeing successful adhesion is extracted for each case, while an overview of the maximum payload is also provided. The validity of the proposed methodology is evaluated through comparative simulations.