This paper presents a new type of underactuated ground mobile robot called Caster Car. The platform consists of a front-driven and steered wheel and two uncontrolled rear caster wheels. The Caster Car model presented can be an interesting alternative for mobile robots that connects dynamic properties of hovercrafts and classical 4-wheeled cars. Underactuated properties of the Caster Car cause that classical proportional-derivative feedback control give the ability to affect only selected configuration variables. Three mathematical models of the Caster Car are proposed: a dynamic model with free-moving casters, a dynamic model with blocked casters, and a simplified hovercraft description. Models were tested during tracking tasks with demanding trajectory using selective and full-state control. This full state control was based on the computed torque technique with the pseudoinverse operation and proportional-derivative feedback. It gives the ability to suppress unstable behaviors of uncontrolled orientation but in cost of overall effect (higher position errors).